Distributive Law

Q. The expression $\sim (\sim p\to q)$ is logically equivalent to :

1. $p\wedge q$
2. $\sim p\wedge q$
3. $\sim p\wedge \sim q$
4. $p\wedge \sim q$

Q. The negation of the Boolean expression $p\vee (\sim p\wedge q)$ is equivalent to:

1. $p\vee \sim q$
2. $\sim p\vee \sim q$
3. $\sim p\vee q$
4. $\sim p\wedge \sim q$

Q. $\sim (p\vee q)\vee (\sim p\wedge q)$ is logically equivalent to ?

1. $\sim q$
2. $\sim p$
3. $p$
4. $q$

Q. For any two statements $pandq$, the negation of the expression $p\vee (\sim p\wedge q)$ is :

1. $\sim p\vee \sim q$
2. $\sim p\wedge \sim q$
3. $p\leftrightarrow q$
4. $p\vee q$

Q. Which of the following is equivalent to the Boolean expression p $\wedge \sim q$?

1. $\sim (q\to p)$
2. $\sim (p\to \sim q)$
3. $\sim (p\to q)$
4. $\sim p\to \sim q$

Q.

The cube root of $0.001$

1. ${10}^{-1}$

2. ${10}^{-2}$

3. ${10}^{-3}$

4. none of these

Q. The negation of the Boolean expression $x\leftrightarrow \sim y$ is equivalent to

1. $(x\wedge y)\wedge (\sim x\vee \sim y)$
2. $(x\wedge y)\vee (\sim x\wedge \sim y)$
3. $(x\wedge \sim y)\vee (\sim x\wedge y)$
4. $(\sim x\wedge y)\vee (\sim x\wedge \sim y)$

Q. The negation of the compound proposition $p\vee (\sim p\vee q)$ is

1. $(p\wedge \sim q)\wedge \sim p$
2. $(p\wedge \sim q)\vee \sim p$
3. $(p\vee \sim q)\vee \sim p$
4. None of these

Q. The expression $\sim (p\vee q)\vee (\sim p\wedge q)$ is logically equivalent to

1. $p$
2. $q$
3. $\sim p$
4. $\sim q$

Q. The logical statement $\sim (\sim p\to q)\vee (p\wedge \sim q)$ is equivalent to

1. $p$
2. $q$
3. $\sim p$
4. $\sim q$

Q. The negation of the logical statement $(p\to q)\to q$ is

1. a tautology
2. a fallacy
3. $\sim (p\vee q)$
4. $p\wedge q$

Q. The negation of $(p\vee q)\wedge (q\vee \sim r)$ is

1. $(\sim p\wedge \sim q)\vee (q\wedge \sim r)$
2. $(\sim p\wedge \sim q)\vee (\sim q\wedge r)$
3. $(\sim p\wedge \sim q)\vee (\sim q\wedge r)$
4. $(p\wedge q)\vee (\sim q\wedge \sim r)$

Q. The logical statement $\sim (\sim p\to q)\vee (p\wedge \sim q)$ is equivalent to

1. $p$
2. $q$
3. $\sim p$
4. $\sim q$

Q. The negation of the compound proposition $p\vee (\sim p\vee q)$ is

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

Q. $\sim \left(\right(\sim p)\wedge q)$ is equal to

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

Q. The negation of the logical statement $(p\to q)\to q$ is

1. a tautology
2. a fallacy
3. $\sim (p\vee q)$
4. $p\wedge q$

Q. Let $p,q,r$ denote the arbitary statements then, the logical equivalance of the statement $p\Rightarrow (q\vee r)$ is

1. $(p\vee q)\Rightarrow r$
2. $(p\Rightarrow q)\vee (p\Rightarrow r)$
3. $(p\Rightarrow q)\wedge (p\Rightarrow r)$
4. $(p\Rightarrow q)\wedge (p\Rightarrow \sim r)$

Q. The proposition $p\to \sim (p\wedge \sim q)$ is equivalent to

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

Q. Which of following is the negation of $(P\vee \sim Q).$

1. $\sim P\vee Q$
2. $\sim Q\wedge P$
3. $\sim P\wedge Q$
4. $\sim Q\vee P$

Q. The negation of the statement $\sim p\wedge (p\vee q)$ is

1. $\sim p\wedge q$
2. $p\wedge \sim q$
3. $\sim p\vee q$
4. $p\vee \sim q$

Q. The negation of $(p\vee q)\wedge (q\vee \sim r)$ is

1. $(\sim p\wedge \sim q)\vee (q\wedge \sim r)$
2. $(\sim p\wedge \sim q)\vee (\sim q\wedge r)$
3. $(\sim p\wedge \sim q)\vee (\sim q\wedge r)$
4. $(p\wedge q)\vee (\sim q\wedge \sim r)$

Q. The expression $\sim (p\vee q)\vee (\sim p\wedge q)$ is logically equivalent to

1. $\sim p$
2. $q$
3. $p$
4. $\sim q$

Q. The Boolean expression $\sim (p\Rightarrow (\sim q\left)\right)$ is equivalent to :

1. $(\sim p)\Rightarrow q$
2. $q\Rightarrow \sim p$
3. $p\wedge q$
4. $p\vee q$

Q. Negation of the statement $\sim p\to (q\vee r)$ is

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

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

1. $p\wedge q$
2. $p\wedge \sim q$
3. $\sim p\wedge q$
4. $\sim p\wedge \sim q$