1
JEE Main 2014 (Offline)
+4
-1
The statement $$\sim \left( {p \leftrightarrow \sim q} \right)$$ is
A
equivalent to $${ \sim p \leftrightarrow q}$$
B
a tautology
C
a fallacy
D
equivalent to $${p \leftrightarrow q}$$
2
JEE Main 2013 (Offline)
+4
-1
Consider :
Statement − I : $$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$$ is a fallacy.
Statement − II :$$\left( {p \to q} \right) \leftrightarrow \left( { \sim q \to \sim p} \right)$$ is a tautology.
A
Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I
B
Statement -I is True; Statement -II is False.
C
Statement -I is False; Statement -II is True
D
Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I
3
AIEEE 2012
+4
-1
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
B
Either I will not become a teacher or I will not open a school
C
Neither I will become a teacher nor I will open a school
D
I will not become a teacher or I will open a school
4
AIEEE 2011
+4
-1
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 and only if Suman is rich” can be expressed as :
A
$$\sim \left[ {Q \leftrightarrow \left( {P \wedge \sim R} \right)} \right]$$
B
$$\sim Q \leftrightarrow P \wedge R$$
C
$$\sim \left( {P \wedge \sim R} \right) \leftrightarrow Q$$
D
$$\sim P \wedge \left( {Q \leftrightarrow \sim R} \right)$$
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