
If \[S(p,q,r)=(\tilde{\ }p)\vee [\tilde{\ }(q\wedge r)]\] is a compound statement, then \[S(\tilde{\ }p,\tilde{\ }q,\tilde{\ }r)\] is
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
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Which of the following is the inverse of the proposition: ?if a number is a prime then it is odd.??
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 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
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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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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
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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
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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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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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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
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If p : It is snowing, q : I am cold, then the compound statement 'it is snowing and it is not that I am cold'? is given by
A)
\[p\wedge (\tilde{\ }q)\] done
clear
B)
\[p\wedge q\] done
clear
C)
\[(\tilde{\ }p)\wedge q\] done
clear
D)
\[(\tilde{\ }p)\wedge (\tilde{\ }q)\] done
clear
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Consider the statement p: 'New Delhi is 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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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
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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
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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
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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
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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
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Let p and q be any two logical statements and \[r:p\to (\tilde{\ }p\vee q).\] If r has a truth value F, then the truth values of p and q are respectively:
A)
F, F done
clear
B)
T, T done
clear
C)
T, F done
clear
D)
F, T done
clear
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If :p Raju is tall and q: Raju is intelligent, then the symbolic statement \[\tilde{\ }p\vee q\] means
A)
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
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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_arrow

If \[p\Rightarrow (q\vee r)\] is false, then the truth values of \[p,q,r\] are respectively
A)
\[T,F,F\] done
clear
B)
\[F,F,F\] done
clear
C)
\[F,T,T\] done
clear
D)
\[T,T,F\] done
clear
View Solution play_arrow

Consider the two statements p: he is intelligent and Q: He is strong. Then the symbolic form of the statement ?It is not true that he is either intelligent or strong?? is
A)
\[\tilde{\ }p\vee Q\] done
clear
B)
\[\tilde{\ }P\wedge \tilde{\ }Q\] done
clear
C)
\[\tilde{\ }P\wedge Q\] done
clear
D)
\[\tilde{\ }(P\vee Q)\] done
clear
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If p: Ashok works hard q: Ashok gets good grade The verbal form for \[(\tilde{\ }p\to q)\] is
A)
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_arrow

For integers m and n, both greater than 1, consider three following three statements:
P: 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_arrow

If \[p\Rightarrow (\tilde{\ }p\,\vee \,q)\] is false, the truth values of p and q are respectively
A)
\[F,T\] done
clear
B)
\[F,F\] done
clear
C)
\[T,T\] done
clear
D)
\[T,F\] done
clear
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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
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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_arrow

\[(p\wedge \tilde{\ }q)\wedge (\tilde{\ }p\wedge q)\] 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_arrow

Consider the two statements p: He is intelligent and Q: he is strong. Then the symbolic form of the statement ?it is not true that he is either intelligent or strong?? is
A)
\[\tilde{\ }P\vee Q\] 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_arrow

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
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The propositions \[(p\Rightarrow \tilde{\ }p)\wedge (\tilde{\ }p\Rightarrow p)\] is a
A)
Tautology and contradiction done
clear
B)
Neither tautology nor contradiction done
clear
C)
Contradiction done
clear
D)
Tautology done
clear
View Solution play_arrow

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 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
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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_arrow

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_arrow

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_arrow

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_arrow

In the truth table for the statement \[(p\to q)\leftrightarrow (\tilde{\ }p\vee q),\] the last column has the truth value in the following order is
A)
\[TTFF\] done
clear
B)
\[FFFF\] done
clear
C)
\[TTTT\] done
clear
D)
\[FTFT\] done
clear
View Solution play_arrow

If p: 4 is an even prime number, q: 6 is a divisor of 12 and r: the HCF of 4 and 6 is 2, then which one of the following is true?
A)
\[(p\wedge q)\] 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_arrow

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_arrow

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_arrow

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_arrow

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_arrow

Let p be the proposition: Mathematics is a interesting and let q be the propositions that Mathematics is difficult, then the symbol \[p\wedge q\]means
A)
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_arrow

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_arrow

The contrapositive of the statement, ?If I do not secure good marks then I cannot go for engineering?, is
A)
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_arrow

\[\tilde{\ }(p\Rightarrow q)\Leftrightarrow \tilde{\ }p\vee \tilde{\ }q\] 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_arrow

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_arrow

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_arrow

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_arrow

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_arrow

The statement 'If \[{{2}^{2}}=5\] then I get first class'? is logically equivalent to
A)
\[{{2}^{2}}=5\] 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_arrow

If p and q are two statement then \[(p\leftrightarrow \tilde{\ }q)\] is true when
A)
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
View Solution play_arrow