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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_answer10) Negation is ?2 + 3 = 5 and 8 < 10? is
A) 2 + 3 ? 5 and < 10 done clear
B) 2 + 3 = 5 and 8 ≮ 10 done clear
C) 2 + 3 ? 5 or 8 ≮ 10 done clear
D) None of these done clear
View Solution play_arrowquestion_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
View Solution play_arrowquestion_answer12) The conditional \[(p\wedge q)\] ? 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
View Solution play_arrowquestion_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
View Solution play_arrowA) \[p\wedge q\] done clear
B) \[p\wedge \tilde{\ }q\] done clear
C) \[\tilde{\ }p\wedge q\] done clear
D) \[\tilde{\ }p\ \wedge \tilde{\ }q\] done clear
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowA) True done clear
B) False done clear
C) True if r is false done clear
D) True if q is true done clear
View Solution play_arrowA) True done clear
B) False done clear
C) May be true or false done clear
D) Data insufficient done clear
View Solution play_arrowA) 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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowA) 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
View Solution play_arrowA) \[\tilde{\ }(p\wedge q)\Rightarrow (r\wedge s)\] 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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowA) done clear
B) done clear
C) done clear
D) None of these done clear
View Solution play_arrowA) done clear
B) done clear
C) done clear
D) None of these done clear
View Solution play_arrowquestion_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
View Solution play_arrowA) done clear
B) done clear
C) done clear
D) None of these done clear
View Solution play_arrowA) done clear
B) done clear
C) done clear
D) done clear
View Solution play_arrowquestion_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
View Solution play_arrowA) Tautology and contradiction done clear
B) Neither tautology nor contradiction done clear
C) Contradiction done clear
D) Tautology done clear
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowA) T, F, F done clear
B) F, F, F done clear
C) F, T, T done clear
D) T, T, F done clear
View Solution play_arrowA) \[(p\wedge q)\vee (p\wedge q)\] 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
View Solution play_arrowquestion_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) \[p\vee (\tilde{\ }p)\]U is a tautology done clear
View Solution play_arrowA) F, T done clear
B) F, F done clear
C) T, T done clear
D) T, F done clear
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowquestion_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
View Solution play_arrowA) 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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