A) \[\tilde{\ }S(p,q,r)\] done clear
B) \[S(p,q,r)\] done clear
C) \[p\vee (q\wedge r)\] done clear
D) \[p\vee (q\vee r)\] 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 not 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
View Solution play_arrowquestion_answer3) 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_answer4) Truth value of the statement ?It is false that \[3+3=33\] Or \[1+2=12'\] is
A) T done clear
B) F done clear
C) Both T and F done clear
D) 54 done clear
View Solution play_arrowquestion_answer5) Which of the following statement is a contradiction?
A) \[(\tilde{\ }p\vee \tilde{\ }q)\vee (p\vee \tilde{\ }q)\] done clear
B) \[(p\to q)\vee (p\wedge \tilde{\ }q)\] done clear
C) \[(\tilde{\ }p\wedge q)\wedge (\tilde{\ }q)\] done clear
D) \[(\tilde{\ }p\wedge q)\vee (\tilde{\ }q)\] done clear
View Solution play_arrowquestion_answer6) 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_answer7) 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_answer8) The contrapositive of \[p\to (\tilde{\ }q\to \tilde{\ }r)\] is-
A) \[(\tilde{\ }q\wedge r)\to \tilde{\ }p\] done clear
B) \[(q\to r)\to \tilde{\ }p\] done clear
C) \[(q\vee \tilde{\ }r)\to \tilde{\ }p\] done clear
D) None of these done clear
View Solution play_arrowA) \[p\wedge (\tilde{\ }q)\] done clear
B) \[p\wedge q\] done clear
C) \[(\tilde{\ }p)\wedge q\] done clear
D) \[(\tilde{\ }p)\wedge (\tilde{\ }q)\] done clear
View Solution play_arrowA) 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
View Solution play_arrowquestion_answer11) Which of the following is not a proposition
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_answer12) Which of the following is always true?
A) \[(\tilde{\ }p\vee \tilde{\ }q)\equiv (p\wedge q)\] done clear
B) \[(p\to q)\equiv (\tilde{\ }q\to \tilde{\ }p)\] done clear
C) \[\tilde{\ }(p\to \tilde{\ }q)\equiv (p\wedge \tilde{\ }q)\] done clear
D) \[\tilde{\ }(p\leftrightarrow q)\equiv (p\to q)\to (q\to p)\] done clear
View Solution play_arrowquestion_answer13) The statement \[p\to (q\to p)\]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
View Solution play_arrowquestion_answer14) The inverse of the statement \[(p\wedge \tilde{\ }q)\to r\] is
A) \[\tilde{\ }(p\vee \tilde{\ }q)\to \tilde{\ }r\] done clear
B) \[(\tilde{\ }p\wedge q)\to \tilde{\ }r\] done clear
C) \[(\tilde{\ }p\vee q)\to \tilde{\ }r\] done clear
D) None of these done clear
View Solution play_arrowquestion_answer15) Identify the false statements
A) \[\tilde{\ }[p\vee (\tilde{\ }q)]\equiv (\tilde{\ }p)\vee q\] done clear
B) \[[p\vee q]\vee (\tilde{\ }p)\] is a tautology done clear
C) \[[p\wedge q)\wedge (\tilde{\ }p)\] is a contradiction done clear
D) \[\tilde{\ }[p\vee q]\equiv (\tilde{\ }p)\vee (\tilde{\ }q)\] done clear
View Solution play_arrowA) F, F done clear
B) T, T done clear
C) T, F done clear
D) F, T done clear
View Solution play_arrowA) Raju is not tall or he is intelligent. done clear
B) Raju is tall or he is intelligent done clear
C) Raju is not tall and he is intelligent done clear
D) Raju is not tall implies he is intelligent done clear
View Solution play_arrowquestion_answer18) 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 runs 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_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) \[\tilde{\ }p\vee Q\] done clear
B) \[\tilde{\ }P\wedge \tilde{\ }Q\] done clear
C) \[\tilde{\ }P\wedge Q\] done clear
D) \[\tilde{\ }(P\vee Q)\] done clear
View Solution play_arrowA) If Ashok works hard then gets good grade done clear
B) If Ashok does not work hard then he gets good grade done clear
C) If Ashok does not work hard then he does not get good grade done clear
D) Ashok works hard if and only if he gets grade done clear
View Solution play_arrowP: m divides n |
Q: m divides \[{{n}^{2}}\] |
R: m is prime, then |
A) \[Q\wedge R\to P\] done clear
B) \[P\wedge Q\to R\] done clear
C) \[Q\to R\] done clear
D) \[Q\to P\] 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_answer24) The negation of the statement \[(p\wedge q)\to (\tilde{\ }p\vee r)\]is
A) \[(p\wedge q)\vee (p\vee \tilde{\ }r)\] done clear
B) \[(p\wedge q)\vee (p\wedge \tilde{\ }r)\] done clear
C) \[(p\wedge q)\wedge (p\wedge \tilde{\ }r)\] done clear
D) \[p\vee q\] done clear
View Solution play_arrowquestion_answer25) Let p, q and r be any three logical statements. Which of the following is true?
A) \[\tilde{\ }[p\wedge (\tilde{\ }q)]\equiv (\tilde{\ }p)\wedge q\] done clear
B) \[\tilde{\ }[(p\vee q)\wedge (\tilde{\ }r)\equiv (\tilde{\ }p)\vee (\tilde{\ }q)\vee (\tilde{\ }r)\] done clear
C) \[\tilde{\ }[p\vee (\tilde{\ }q)]\equiv (\tilde{\ }p)\wedge q\] done clear
D) \[\tilde{\ }[p\vee (\tilde{\ }q)]\equiv (\tilde{\ }p)\wedge \tilde{\ }q\] done clear
View Solution play_arrowquestion_answer26) \[(p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)\] is
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_arrowA) \[\tilde{\ }P\vee Q\] done clear
B) \[\tilde{\ }P\wedge \tilde{\ }Q\] done clear
C) \[\tilde{\ }P\wedge Q\] done clear
D) \[\tilde{\ }(P\vee Q)\] done clear
View Solution play_arrowquestion_answer28) 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) \[q\wedge p\] is true done clear
D) \[p\Rightarrow q\] is true 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_arrowA) If a number is neither rational n 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_arrowquestion_answer31) The negation of the statement ?A circle is an ellipse?? is
A) An ellipse is a circle done clear
B) An ellipse is not a circle done clear
C) A circle is not an ellipse done clear
D) A circle is an ellipse done clear
View Solution play_arrowquestion_answer32) Which of the following is false?
A) \[p\vee \tilde{\ }p\] is a tautology done clear
B) \[\tilde{\ }(\tilde{\ }p)\leftrightarrow p\] is a tautology done clear
C) \[p\wedge \tilde{\ }p\] is a contradiction done clear
D) \[((p\wedge q)\to q)\to p\] is a tautology done clear
View Solution play_arrowquestion_answer33) Which of the following is always true?
A) \[(\tilde{\ }p\Rightarrow q)=\tilde{\ }q\Rightarrow \tilde{\ }p\] 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_answer34) 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
View Solution play_arrowA) \[TTFF\] done clear
B) \[FFFF\] done clear
C) \[TTTT\] done clear
D) \[FTFT\] done clear
View Solution play_arrowA) \[(p\wedge q)\] done clear
B) \[(p\vee q)\wedge \tilde{\ }r\] done clear
C) \[\tilde{\ }(q\wedge r)p\] done clear
D) \[\tilde{\ }p\vee (q\wedge r)\] done clear
View Solution play_arrowquestion_answer37) Which of the following is a contradiction?
A) \[(p\wedge q)\wedge \tilde{\ }(p\vee q)\] done clear
B) \[p\vee (-p\wedge q)\] done clear
C) \[(p\Rightarrow q)\Rightarrow p\] done clear
D) None of these done clear
View Solution play_arrowquestion_answer38) Consider the following statements
p: A tumbler is half empty. |
q: A tumbler is half full. |
The, the combination form of 'p if and only if q'? is |
A) A tumbler is half empty and half full done clear
B) A tumbler is half empty if and only if it is hatful done clear
C) Both (a) and (b) done clear
D) None of the above done clear
View Solution play_arrowquestion_answer39) The contrapositive of \[(p\vee q)\Rightarrow r\] is
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_arrowquestion_answer40) The negation of \[(p\vee \tilde{\ }q)\wedge q\] is
A) \[(\tilde{\ }p\vee q)\wedge \tilde{\ }q\] done clear
B) \[(p\wedge \tilde{\ }q)\vee q\] done clear
C) \[(\tilde{\ }p\wedge q)\vee \tilde{\ }q\] done clear
D) \[(p\wedge \tilde{\ }q)\vee \tilde{\ }q\] done clear
View Solution play_arrowA) Mathematics is interesting ipllies that Mathematics is difficult done clear
B) Mathematics is interesting impels and is implied by Mathematics is difficult done clear
C) Mathematics is interesting and Mathematics is difficult done clear
D) Mathematics is interesting or Mathematics is difficult done clear
View Solution play_arrowquestion_answer42) 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) \[\tilde{\ }(\tilde{\ }p\Leftrightarrow q)\equiv [\tilde{\ }(p\Rightarrow q)\wedge \tilde{\ }(q\Rightarrow p)]\] done clear
View Solution play_arrowA) If I secure good marks, then I go for engineering done clear
B) If I go for engineering then I secure good marks done clear
C) If I cannot go for engineering then I do not secure good marks done clear
D) None done clear
View Solution play_arrowquestion_answer44) \[\tilde{\ }(p\Rightarrow q)\Leftrightarrow \tilde{\ }p\vee \tilde{\ }q\] 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_answer45) If p is nay 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
View Solution play_arrowquestion_answer46) The false statement of the following is
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) \[p\vee (\tilde{\ }p)\Leftrightarrow p\] is a tautology done clear
View Solution play_arrowquestion_answer47) Negation of the proposition: If we control population growth, we prosper
A) If we do not control population growth, we prosper done clear
B) If we control population growth, we do not prosper done clear
C) We control population but we do not prosper done clear
D) We do not control population, but we prosper. done clear
View Solution play_arrowquestion_answer48) The inverse of the statement, if x is zero then we cannot divide by x? is
A) If we cannot divide by x, then x is zero done clear
B) If we cannot divide by x, then x is not zero done clear
C) If x is not zero then we divide by x done clear
D) None. done clear
View Solution play_arrowA) \[{{2}^{2}}=5\] and I do not get first class done clear
B) \[{{2}^{2}}=5\] or I do not get first class done clear
C) \[{{2}^{2}}\ne 5\] or I get first class done clear
D) None of these done clear
View Solution play_arrowA) p and q both are true done clear
B) p and q both are false done clear
C) p is false and q is true done clear
D) None of these done clear
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