Negation

Q.

What is the negation of the statement 3 + 7 = 10

1. 3 + 7 = -10

2. 3 + 7 > 10

3. 10 = 3 + 7

4. 3 + 7 ≠ 10

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

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

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

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

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

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

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

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.

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. $\sim P\wedge (Q\leftrightarrow \sim R)$

Q.

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

1. $(\sim p\wedge \sim q)\wedge p$

2. $(p\vee \sim q)\wedge \sim p$

3. $(p\wedge \sim q)\wedge \sim p$

4. $(p\wedge \sim q)\vee \sim p$

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

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

Q.

Negation of the compound statement ‘if the examination is difficult, then I shall pass if I study hard’ is ___.

1. The examination is difficult and I do not study hard and I shall pass

2. The examination is not difficult and I study hard and I shall not pass

3. The examination is difficult and I study hard and I shall not pass

4. The examination is difficult and I study hard and I shall pass