JEE Main & Advanced Mathematics Mathematical Logic and Boolean Algebra Question Bank

done Mathematical Logic Total Questions - 50

• question_answer1)
  Which of the following is a statement
  A)
                  Open the door  done clear
  B)
                  Do your homework done clear
  C)
                  Switch on the fan             done clear
  D)
                  Two plus two is four done clear
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• question_answer2)
  Which of the following is a statement
  A)
                  May you live long ! done clear
  B)
                  May God bless you ! done clear
  C)
                  The sun is a star done clear
  D)
                  Hurrah ! we have won the match done clear
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• question_answer3)
  Which of the following is not a statement
  A)
                  Roses are red    done clear
  B)
                  New Delhi is in India done clear
  C)
                  Every square is a rectangle done clear
  D)
                  Alas ! I have failed done clear
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• question_answer4)
  Which of the following is not a statement
  A)
                  Every set is a finite set done clear
  B)
                  8 is less than 6 done clear
  C)
                  Where are you going? done clear
  D)
                  The sum of interior angles of a triangle is 180 degrees done clear
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• question_answer5)
  Which of the following is not a statement
  A)
                  Please do me a favour   done clear
  B)
                  2 is an even integer done clear
  C)
                  2 + 1 = 3                done clear
  D)
                  The number 17 is prime done clear
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• question_answer6)
  Which of the following is not a statement
  A)
                  Give me a glass of water done clear
  B)
                  Asia is a continent done clear
  C)
                  The earth revolved round the sun done clear
  D)
                  The number 6 has two prime factors 2, 3 done clear
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• question_answer7)
  Which of the following is an open statement
  A)
                  x is a natural number done clear
  B)
                  Give me a glass of water done clear
  C)
                  Wish you best of luck     done clear
  D)
                  Good morning to all done clear
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• question_answer8)
  Negation of the conditional : ?If it rains, I shall go to school? is
  A)
                  It rains and I shall go to school done clear
  B)
                  It rains and I shall not go to school done clear
  C)
                  It does not rains and I shall go to school done clear
  D)
                  None of these done clear
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• question_answer9)
  Negation of ?Paris in France and London is in England? is
  A)
                  Paris is in England and London is in France done clear
  B)
                  Paris is not in France or London is not in England done clear
  C)
                  Paris is in England or London is in France done clear
  D)
                  None of these done clear
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• question_answer10)
  Negation is ?2 + 3 = 5 and 8 < 10? is
  A)
                  2 + 3 ¹ 5 and < 10              done clear
  B)
                  2 + 3 = 5 and 8 ≮ 10 done clear
  C)
                  2 + 3 ¹ 5 or 8 ≮ 10            done clear
  D)
                  None of these done clear
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• question_answer11)
  Negation of ?Ram is in Class X or Rashmi is in Class XII? is
  A)
                  Ram is not in class X but Ram is in class XII done clear
  B)
                  Ram is not in class X but Rashmi is not in class XII done clear
  C)
                  Either Ram is not in class X or Ram is not in class XII done clear
  D)
                  None of these done clear
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• question_answer12)
  The conditional \[(p\wedge q)\] Þ p is
  A)
                  A tautology done clear
  B)
                  A fallacy i.e., contradiction done clear
  C)
                  Neither tautology nor fallacy done clear
  D)
                  None of these done clear
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• question_answer13)
  Which of the following is a contradiction
  A)
                  \[(p\wedge q)\wedge \tilde{\ }(p\vee q)\]         done clear
  B)
                  \[p\vee (\tilde{\ }p\wedge q)\] done clear
  C)
                  \[(p\Rightarrow q)\Rightarrow p\]           done clear
  D)
                  None of these done clear
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• question_answer14)
  Which of the following is logically equivalent to \[\tilde{\ }(\tilde{\ }p\Rightarrow q)\]
  A)
                  \[p\wedge q\]  done clear
  B)
                  \[p\wedge \tilde{\ }q\] done clear
  C)
                  \[\tilde{\ }p\wedge q\] done clear
  D)
                  \[\tilde{\ }p\ \wedge \tilde{\ }q\] done clear
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• question_answer15)
  \[\tilde{\ }(p\vee q)\] is equal to
  A)
                  \[\tilde{\ }p\ \vee \tilde{\ }q\]   done clear
  B)
                  \[\tilde{\ }p\ \wedge \tilde{\ }q\] done clear
  C)
                  \[\tilde{\ }p\vee q\]       done clear
  D)
                  \[p\ \vee \tilde{\ }q\] done clear
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• question_answer16)
  \[\tilde{\ }(p\wedge q)\] is equal to                       
  A)
                  \[\tilde{\ }p\ \vee \tilde{\ }q\] done clear
  B)
                  \[\tilde{\ }p\ \wedge \tilde{\ }q\] done clear
  C)
                  \[\tilde{\ }p\wedge q\] done clear
  D)
                  \[p\ \wedge \tilde{\ }q\] done clear
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• question_answer17)
  \[(\tilde{\ }(\tilde{\ }p))\wedge q\] is equal to
  A)
                  \[\tilde{\ }p\wedge q\] done clear
  B)
                  \[p\wedge q\] done clear
  C)
                  \[p\ \wedge \tilde{\ }q\]              done clear
  D)
                  \[\tilde{\ }p\ \wedge \tilde{\ }q\] done clear
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• question_answer18)
  \[\tilde{\ }(p\vee (\tilde{\ }q))\] is equal to
  A)
                  \[\tilde{\ }p\vee q\]       done clear
  B)
                  \[(\tilde{\ }p)\wedge q\] done clear
  C)
                  \[\tilde{\ }p\ \vee \tilde{\ }p\]   done clear
  D)
                  \[\tilde{\ }p\ \wedge \tilde{\ }q\] done clear
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• question_answer19)
  \[\tilde{\ }((\tilde{\ }p)\ \wedge q)\] is equal to
  A)
                  \[p\vee (\tilde{\ }q)\]    done clear
  B)
                  \[p\vee q\] done clear
  C)
                  \[p\wedge (\tilde{\ }q)\]              done clear
  D)
                  \[\tilde{\ }p\ \wedge \tilde{\ }q\] done clear
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• question_answer20)
  \[\tilde{\ }(p\Leftrightarrow q)\] is
  A)
                  \[\tilde{\ }p\ \wedge \tilde{\ }q\]             done clear
  B)
                  \[\tilde{\ }p\ \vee \tilde{\ }q\] done clear
  C)
                  \[(p\ \wedge \tilde{\ }q)\vee (\tilde{\ }p\ \wedge q)\]  done clear
  D)
                  None of these done clear
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• question_answer21)
  \[p\Rightarrow q\] can also be written as
  A)
                  \[p\Rightarrow \ \tilde{\ }q\]      done clear
  B)
                  \[\tilde{\ }p\vee q\] done clear
  C)
                  \[\tilde{\ }q\Rightarrow \tilde{\ }p\]       done clear
  D)
                  None of these done clear
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• question_answer22)
  If p, q, r are simple propositions with truth values T, F, T, then the truth value of \[(\tilde{\ }p\vee q)\ \wedge \tilde{\ }r\Rightarrow p\] is
  A)
                  True       done clear
  B)
                  False done clear
  C)
                  True if r is false  done clear
  D)
                  True if q is true done clear
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• question_answer23)
  If \[(p\ \wedge \tilde{\ }r)\Rightarrow (q\vee r)\] is false and q and r are both false, then p is
  A)
                  True       done clear
  B)
                  False done clear
  C)
                  May be true or false       done clear
  D)
                  Data insufficient done clear
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• question_answer24)
  If p, q, r are simple propositions, then \[(p\wedge q)\wedge (q\wedge r)\] is true then
  A)
                  p, q, r are all false             done clear
  B)
                  p, q, r are all true done clear
  C)
                  p, q are true and r is false done clear
  D)
                  p is true and q and r are false done clear
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• question_answer25)
  \[\tilde{\ }(p\Rightarrow q)\Leftrightarrow \tilde{\ }p\ \vee \tilde{\ }q\] is
  A)
                  A tautology done clear
  B)
                  A contradiction done clear
  C)
                  Neither a tautology nor a contradiction done clear
  D)
                  Cannot come to any conclusion done clear
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• question_answer26)
  \[(p\ \wedge \tilde{\ }q)\wedge (\tilde{\ }p\vee q)\] is
  A)
                  A contradiction done clear
  B)
                  A tautology done clear
  C)
                  Either A or B       done clear
  D)
                  Neither A nor B done clear
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• question_answer27)
  Which of the following is not logically equivalent to the proposition : ?A real number is either rational or irrational?.
  A)
                  If a number is neither rational nor irrational then it is not real done clear
  B)
                  If a number is not a rational or not an irrational, then it is not real done clear
  C)
                  If a number is not real, then it is neither rational nor irrational done clear
  D)
                  If a number is real, then it is rational or irrational done clear
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• question_answer28)
  If p : It rains today, q : I go to school, r : I shall meet any friends and s : I shall go for a movie, then which of the following is the proposition : If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.
  A)
                  \[\tilde{\ }(p\wedge q)\Rightarrow (r\wedge s)\]            done clear
  B)
                  \[\tilde{\ }(p\ \wedge \tilde{\ }q)\Rightarrow (r\wedge s)\] done clear
  C)
                  \[\tilde{\ }(p\ \wedge q)\ \Rightarrow (r\vee s)\]             done clear
  D)
                  None of these done clear
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• question_answer29)
  The negation of the compound proposition \[p\vee (\tilde{\ }p\vee q)\] is
  A)
                  \[(p\ \wedge \tilde{\ }q)\ \wedge \tilde{\ }p\]   done clear
  B)
                  \[(p\ \wedge \tilde{\ }q)\ \vee \tilde{\ }p\] done clear
  C)
                  \[(p\ \vee \tilde{\ }q)\ \vee \tilde{\ }p\]               done clear
  D)
                  None of these done clear
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• question_answer30)
  Which of the following is true
  A)
                  \[p\Rightarrow q\equiv \ \tilde{\ }p\Rightarrow \ \tilde{\ }q\] done clear
  B)
                  \[\tilde{\ }(p\Rightarrow \ \tilde{\ }q)\equiv \ \tilde{\ }p\wedge q\] done clear
  C)
                  \[\tilde{\ }(\tilde{\ }p\Rightarrow \,\tilde{\ }q)\equiv \tilde{\ }p\wedge q\] done clear
  D)
                  \[\tilde{\ }(p\Leftrightarrow q)\equiv [\tilde{\ }(p\Rightarrow q)\wedge \tilde{\ }(q\Rightarrow p)]\] done clear
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• question_answer31)
  \[\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)\] is logically equivalent to
  A)
                  ~p           done clear
  B)
                  p done clear
  C)
                  q             done clear
  D)
                  ~q done clear
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• question_answer32)
  The inverse of the proposition \[(p\ \wedge \tilde{\ }q)\Rightarrow r\] is
  A)
                  \[\tilde{\ }r\Rightarrow \ \tilde{\ }p\vee q\]        done clear
  B)
                  \[\tilde{\ }p\vee q\Rightarrow \ \tilde{\ }r\] done clear
  C)
                  \[r\Rightarrow p\ \wedge \tilde{\ }q\]   done clear
  D)
                  None of these done clear
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• question_answer33)
  When does the current flow through the following circuit
  A)
                  p, q, r should be closed done clear
  B)
                  p, q, r should be open done clear
  C)
                  Always done clear
  D)
                  None of these done clear
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• question_answer34)
  Which Venn diagram represent the truth of the statement ?All students are hard working.? Where U = Universal set of human beings                      S = Set of all students                      H = Set of all hard workers
  A)
                 done clear
  B)
    done clear
  C)
                 done clear
  D)
                  None of these done clear
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• question_answer35)
  Which Venn diagram represent the truth of the statements ?No child is naughty? Where U = Universal set of human beings                     C = Set of children                     N = Set of naughty persons
  A)
                 done clear
  B)
    done clear
  C)
    done clear
  D)
                  None of these done clear
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• question_answer36)
  Which Venn diagram represent the truth of the statement ?No policeman is a thief?
  A)
                 done clear
  B)
    done clear
  C)
                 done clear
  D)
                  None of these done clear
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• question_answer37)
  Which Venn diagram represent the truth of the statement ?Some teenagers are not dreamers?
  A)
                 done clear
  B)
    done clear
  C)
                 done clear
  D)
                  None of these done clear
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• question_answer38)
  Which of the following Venn diagram corresponds to the statement ?All mothers are women? (M is the set of all mothers, W is the set of all women)
  A)
                 done clear
  B)
    done clear
  C)
                 done clear
  D)
    done clear
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• question_answer39)
  The negative of \[q\ \vee \tilde{\ }(p\wedge r)\] is                          [Karnataka CET 1997]
  A)
                  \[\tilde{\ }q\ \wedge \tilde{\ }(p\wedge r)\]       done clear
  B)
                  \[\tilde{\ }q\wedge (p\wedge r)\] done clear
  C)
                  \[\tilde{\ }q\vee (p\wedge r)\] done clear
  D)
                  None of these done clear
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• question_answer40)
  The propositions \[(p\Rightarrow \ \tilde{\ }p)\wedge (\tilde{\ }p\Rightarrow p)\] is a    [Karnataka CET 1997]
  A)
                  Tautology and contradiction done clear
  B)
                  Neither tautology nor contradiction done clear
  C)
                  Contradiction done clear
  D)
                  Tautology done clear
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• question_answer41)
  Which of the following is always true      [Karnataka CET 1998]
  A)
                  \[(p\Rightarrow q)\equiv \ \tilde{\ }q\Rightarrow \ \tilde{\ }p\] done clear
  B)
                  \[\tilde{\ }(p\vee q)\equiv \vee \ p\ \vee \tilde{\ }q\] done clear
  C)
                  \[\tilde{\ }(p\Rightarrow q)\equiv p\ \wedge \tilde{\ }q\]            done clear
  D)
                  \[\tilde{\ }(p\vee q)\equiv \ \tilde{\ }p\ \ \wedge \tilde{\ }q\] done clear
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• question_answer42)
  The contrapositive of \[(p\vee q)\Rightarrow r\] is          [Karnataka CET 1999]
  A)
                  \[r\Rightarrow (p\vee q)\]          done clear
  B)
                  \[\tilde{\ }r\Rightarrow (p\vee q)\] done clear
  C)
                  \[\tilde{\ }r\Rightarrow \ \tilde{\ }p\ \wedge \tilde{\ }q\]             done clear
  D)
                  \[p\Rightarrow (q\vee r)\] done clear
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• question_answer43)
  If \[p\Rightarrow (q\vee r)\] is false, then the truth values of p, q, r are respectively                                       [Karnataka CET 2000]
  A)
                  T, F, F    done clear
  B)
                  F, F, F done clear
  C)
                  F, T, T    done clear
  D)
                  T, T, F done clear
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• question_answer44)
  The logically equivalent proposition of \[p\Leftrightarrow q\] is [Karnataka CET 2000]
  A)
                  \[(p\wedge q)\vee (p\wedge q)\]           done clear
  B)
                  \[(p\Rightarrow q)\wedge (q\Rightarrow p)\] done clear
  C)
                  \[(p\wedge q)\vee (q\Rightarrow p)\]  done clear
  D)
                  \[(p\wedge q)\Rightarrow (q\vee p)\] done clear
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• question_answer45)
  The false statement in the following is [Karnataka CET 2002]
  A)
                  \[p\wedge (\tilde{\ }p)\] is a contradiction done clear
  B)
                  \[(p\Rightarrow q)\Leftrightarrow (\tilde{\ }q\Rightarrow \ \tilde{\ }p)\] is a contradiction done clear
  C)
                  \[\tilde{\ }(\tilde{\ }p)\Leftrightarrow p\] is a tautology done clear
  D)
                  \[p\vee (\tilde{\ }p)\]Û is a tautology done clear
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• question_answer46)
  If \[p\Rightarrow (\tilde{\ }p\vee q)\] is false, the truth values of p and q are respectively                                            [Karnataka CET 2002]
  A)
                  F, T         done clear
  B)
                  F, F done clear
  C)
                  T, T         done clear
  D)
                  T, F done clear
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• question_answer47)
  Which of the following is not a proposition [Karnataka CET 2002]
  A)
                  \[\sqrt{3}\] is a prime     done clear
  B)
                  \[\sqrt{2}\] is irrational done clear
  C)
                  Mathematics is interesting done clear
  D)
                  5 is an even integer done clear
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• question_answer48)
  \[(p\ \wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)\] is                                           [Karnataka CET 2003]
  A)
                  A tautology done clear
  B)
                  A contradiction done clear
  C)
                  Both a tautology and a contradiction done clear
  D)
                  Neither a tautology nor a contradiction done clear
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• question_answer49)
  \[\tilde{\ }p\wedge q\] is logically equivalent to                [Karnataka CET 2004]
  A)
                  \[p\to q\]            done clear
  B)
                  \[q\to p\] done clear
  C)
                  \[\tilde{\ }(p\to q)\]       done clear
  D)
                  \[\tilde{\ }(q\to p)\] done clear
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• question_answer50)
  Which of the following is the inverse of the proposition: ?If a number is a prime then it is odd.?  [Karnataka CET 2004]
  A)
                  If a number is not a prime then it is odd done clear
  B)
                  If a number is not a prime then it is odd done clear
  C)
                  If a number is not odd then it is not a prime done clear
  D)
                  If a number is not odd then it is a prime done clear
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