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

done Mock Test - Mathematical Reasoning Total Questions - 25

• question_answer1)
  Consider the statement p: 'New Delhi is a city'. Which of the following is not negation of p?
  A)
  New Delhi is not a city done clear
  B)
  It is false that New Delhi is a city done clear
  C)
  It is not the case that New Delhi is a city done clear
  D)
  None of these done clear
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• question_answer2)
  The contrapositive of the inverse of \[p\Rightarrow \,\tilde{\ }q\]is
  A)
  \[\tilde{\ }q\Rightarrow p\] done clear
  B)
  \[p\Rightarrow q\] done clear
  C)
  \[\tilde{\ }q\Rightarrow \,\tilde{\ }p\]         done clear
  D)
  \[\tilde{\ }p\Rightarrow \,\tilde{\ }q\] done clear
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• question_answer3)
  If p is any statement, then which of the following is a tautology?
  A)
  \[p\wedge f\]       done clear
  B)
  \[p\vee f\] done clear
  C)
  \[p\vee (\tilde{\ }p)\]        done clear
  D)
  \[p\wedge t\] done clear
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• question_answer4)
  Which of the following is the contrapositive of 'if two triangles are identical, then these are similar'?
  A)
  if two triangles are not similar, then are not identical done clear
  B)
  If two triangles are not identical, then these are not similar done clear
  C)
  If two triangles are not identical, then these are similar done clear
  D)
  If two triangles are not similar, then these are identical done clear
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• question_answer5)
  Contrapositive of the statement \[p\Rightarrow q\] is
  A)
  \[\tilde{\ }q\Rightarrow \,\tilde{\ }p\]         done clear
  B)
  \[p\Leftrightarrow q\] done clear
  C)
  \[q\Rightarrow p\] done clear
  D)
  None of these done clear
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• question_answer6)
  If p is true and q is false, then which of the following statements is not true?
  A)
  \[p\vee q\]          done clear
  B)
  \[p\Rightarrow q\] done clear
  C)
  \[p\wedge (\tilde{\ }q)\] done clear
  D)
  \[p\Rightarrow p\] done clear
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• question_answer7)
  \[\tilde{\ }(p\vee q)\vee (\tilde{\ }p\wedge q)\] is equivalent to
  A)
  q                      done clear
  B)
  p done clear
  C)
  ~p        done clear
  D)
  ~q done clear
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• question_answer8)
  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_answer9)
  If \[(p\wedge \tilde{\ }r)\wedge (\tilde{\ }p/q)\] is false, then the truth values of p, q and r, respectively
  A)
  T, F and F         done clear
  B)
  F. F and T done clear
  C)
  F, T and T         done clear
  D)
  T. F and T done clear
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• question_answer10)
  If p and q are two statements, then \[(p\Rightarrow q)\Leftrightarrow (\tilde{\ }q\Rightarrow \tilde{\ }p)\]is a
  A)
  contradiction      done clear
  B)
  tautology done clear
  C)
  neither [a] nor [b] done clear
  D)
  none of the above done clear
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• question_answer11)
  The logically equivalent proposition of \[p\Rightarrow q\]is
  A)
  \[(p\Rightarrow q)\vee (q\Rightarrow p)\] done clear
  B)
  \[(p~\vee \,q)\Rightarrow (p\vee q)\] done clear
  C)
  \[(p~\wedge \,q)~\vee \,(p~\vee \,q)\]       done clear
  D)
  \[(p~\Rightarrow q)~\wedge \,(q\Rightarrow p)\] done clear
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• question_answer12)
  If both p and q are false, then
  A)
  \[p\wedge q\]is true          done clear
  B)
  \[p\vee q\]is false done clear
  C)
  \[p\Rightarrow q\]is true    done clear
  D)
  None of these done clear
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• question_answer13)
  The logically equivalent proposition of póq is
  A)
  \[(p\Rightarrow q)\vee (p\wedge q)\] done clear
  B)
  \[(p\Rightarrow q)\wedge (q\Rightarrow p)\] done clear
  C)
  \[(p\wedge q)\wedge (q\Rightarrow p)\] done clear
  D)
  \[(p\wedge q)\Rightarrow (p\vee q)\] done clear
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• question_answer14)
  If each of the following statements is true, then \[P\Rightarrow \tilde{\ }q,\text{ }q\Rightarrow r,\text{ }\tilde{\ }r\]
  A)
  p is false done clear
  B)
  p is true done clear
  C)
  q is true done clear
  D)
  None of these done clear
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• question_answer15)
  Which of the following is a statement?
  A)
  \[\tilde{\ }(p\vee q)\equiv p\vee \tilde{\ }q\] done clear
  B)
  \[(p\Rightarrow q)\equiv \,\,\tilde{\ }q\Rightarrow \,\tilde{\ }p\] 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_answer16)
  If p is false and q is true, then
  A)
  \[p\wedge q\] is true         done clear
  B)
  \[p\,\vee \tilde{\ }q\]is true done clear
  C)
  \[q\wedge q\]is true          done clear
  D)
  \[p\Rightarrow q\]is true done clear
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• question_answer17)
  What is negation of the compound proposition? If the examination is difficult, then I shall pass if I study hard.
  A)
  The examination is difficult and I study hard but I shall not pass done clear
  B)
  The examination is difficult and I study hard and I shall pass done clear
  C)
  The examination is not difficult and I study hard and I shall pass done clear
  D)
  None of these done clear
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• question_answer18)
  \[(p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\vee ~q)\]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_answer19)
  The statement \[p\to (p\to q)\]is equivalent to
  A)
  \[p\to (p\to q)\]   done clear
  B)
  \[p\to (p\,\vee q)\] done clear
  C)
  \[p\to (p\,\wedge q)\]        done clear
  D)
  \[p\to (p\leftrightarrow q)\] done clear
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• question_answer20)
  Let S be a non-empty subset of R. Consider the following statement: P: There is a rational number \[x\in S\] such that\[x>0\]. Which of the following statements is the negation of the statement p?
  A)
  \[x\in S\] and \[x\le 0\Rightarrow x\] is not rational. done clear
  B)
  There is a rational number \[x\in S\] such that \[x\le 0\]. done clear
  C)
  There is no rational number \[x\in S\] such that\[x\le 0\]. done clear
  D)
  Every rational number \[x\in S\]satisfies\[x\le 0\]. done clear
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• question_answer21)
  The negation of the statement "If I become a teacher, then I will open a school", is:
  A)
  I will become a teacher and I will not open a school. done clear
  B)
  Either I will not become a teacher or I will not open a school. done clear
  C)
  Nither I will not become a teacher or I will not open a school done clear
  D)
  I will not become a teacher or I will open a school. done clear
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• question_answer22)
  The statement \[\tilde{\ }(p\leftrightarrow \tilde{\ }q)\]is
  A)
  equivalent to \[p\leftrightarrow q\] done clear
  B)
  equivalent to ~\[p\leftrightarrow q\] done clear
  C)
  a tautology done clear
  D)
  a fallacy done clear
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• question_answer23)

  Consider the following statements

  P: Suman is brilliant

  Q: Suman is rich

  R: Suman is honest

  The negation of the statement "Suman is brilliant  and dishonest if any only if suman is rich" can be expressed as

   
  A)
  \[\tilde{\ }(P\wedge \tilde{\ }R)\leftrightarrow Q\] done clear
  B)
  \[\tilde{\ }(P\wedge (Q\leftrightarrow \,\tilde{\ }R)\] done clear
  C)
  \[\tilde{\ }(Q\leftrightarrow (P\wedge \tilde{\ }R))\] done clear
  D)
  \[\tilde{\ }Q\leftrightarrow \,\tilde{\ }P\wedge R\] done clear
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• question_answer24)
  The Boolean Expression \[(p\wedge \tilde{\ }q)\vee q\vee (\tilde{\ }p\wedge q)\]is equivalent to
  A)
  \[p\wedge q\]      done clear
  B)
  \[p\vee q\] done clear
  C)
  \[p\,\vee \tilde{\ }q\]        done clear
  D)
  \[\tilde{\ }p\wedge q\] done clear
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• question_answer25)
  The following statement \[(p\to q)\to [(\tilde{\ }p\to q)\to q]\]is
  A)
  a fallacy done clear
  B)
  a tautology done clear
  C)
  equivalent to \[\tilde{\ }p\to q\] done clear
  D)
  equivalent to \[p\to \tilde{\ }q\] done clear
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