1
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
$$\sim P \wedge \left( {Q \leftrightarrow \sim R} \right)$$
2
AIEEE 2010
+4
-1
Let S be a non-empty subset of R. Consider the following statement:
P : There is a rational number x ∈ S such that x > 0.
Which of the following statements is the negation of the statement P ?
A
There is no rational number x ∈ S such that x ≤ 0
B
Every rational number x ∈ S satisfies x ≤ 0
C
x ∈ S and x ≤ 0 $$\Rightarrow$$ x is not rational
D
There is a rational number x ∈ S such that x ≤ 0
3
AIEEE 2009
+4
-1
Statement-1 : $$\sim \left( {p \leftrightarrow \sim q} \right)$$ is equivalent to $${p \leftrightarrow q}$$.
Statement-2 : $$\sim \left( {p \leftrightarrow \sim q} \right)$$ is a tautology.
A
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1
B
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1
C
Statement-1 is true, Statement-2 is false
D
Statement-1 is false, Statement-2 is true
4
AIEEE 2008
+4
-1
Let p be the statement “x is an irrational number”, q be the statement “y is a transcendental number”, and r be the statement “x is a rational number iff y is a transcendental number”.

Statement –1: r is equivalent to either q or p.

Statement –2: r is equivalent to $$\sim \left( {p \leftrightarrow \sim q} \right)$$
A
Statement − 1 is true, Statement − 2 is false
B
Statement −1 is false, Statement −2 is true
C
Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
D
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1
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