And

Q. Let statement $(p\to q)\to (\sim q\wedge r)$ is false If statement p is true then statement r will be

1. False
2. May be true or may be false
3. True
4. None

Q.

$(p\wedge \sim q)\wedge (\sim p\wedge q)$ is ___.

1. A tautology

2. A fallacy

3. Both a tautology and a fallacy

4. Neither a tautology nor a fallacy

Q. In which of the following cases is $(p\wedge q)\vee (\stackrel{}{\tilde{p}}\wedge \tilde{q})$ true?

1. p is true, q is false.
2. p is false, q is true.
3. Both p and q are true.
4. Both p and q are false.

Q. Which of the following is logically equivalent to $(p\wedge q)$ ?

1. $p\to \sim q$
2. $\sim p\vee \sim q$
3. $\sim \left(p\to \sim q\right)$
4. $\sim \left(\sim p\wedge \sim q\right)$

Q.

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

1. $\sim (Q\leftrightarrow (P\wedge \sim R\left)\right)$
2. $\sim Q\leftrightarrow \sim P\wedge R$
3. $\sim (P\wedge \sim R)\leftrightarrow Q$
4. $\sim P\wedge (Q\leftrightarrow \sim R)$