Negation

Q. The negation of $\sim s\vee (\sim r\wedge s)$ is equivalent to

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

Q.

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

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

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

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

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

Q. Write the negation of the following statements: (i) Chennai is the capital of Tamil Nadu. (ii) is not a complex number. (iii) All triangles are not equilateral triangle. (iv) The number 2 is greater than 7. (v) Every natural number is an integer.

Q.

Let p, q, and r be any three logical statements. Which of the following is true?

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

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

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

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

Q.

If $p:7$is not greater than 4 and $q:$Paris is in France, are two statements. Then, $~(p\vee q)$ is the statement :

1. $7$ is greater than $4$ or Paris is not in France

2. $7$ is not greater than $4$ and Paris is not in France

3. $7$ is greater than $4$ and Paris is in France

4. $7$is not greater than $4$ or Paris is not in France

5. $7$ is greater than $4$ and Paris is not in France

Q.

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

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

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

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

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

Q.

Two statements p and q are given below.

p: 7 is not greater than 4
q: Paris is in France

Then the statement $\sim (p\vee q)is$

1. 7 is greater than 4 or Paris is not in France

2. 7 is greater than 4 and Paris is not in France

3. 7 is not greater than 4 and Paris is not in France

4. 7 is not greater than 4 or Paris is not in France

Q.

Let p, q, r be three statements. Then $\sim (p\vee (q\wedge r\left)\right)$ is equal to

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

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

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

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

Q.

If S(p, q, r)=$\sim p\vee \sim (q\vee r)$ is a compund statement, then S(~p, ~q, ~r) is

1. ~S (p, q, r)

2. S(p, q, r)

3. $p\vee (q\wedge r)$

4. $p\vee (q\vee r)$

Q.

$\sim (\sim p\wedge q)$ is logically equivalent to

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

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

3. $p\vee \sim q$

4. $p\wedge \sim q$

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

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

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

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

Q.

Two statements p and q are given below.

p: 2 plus 3 is 5
q: Delhi is the capital of India

Then the statement "Delhi is the capital of India and it is not that 2 plus 3 is five" is

1. $\sim p\vee q$

2. $\sim p\wedge q$

3. $p\wedge \sim q$

4. $p\vee \sim q$

Q. Are the following pairs of statements negations of each other? (i) The number x is not a rational number. The number x is not an irrational number. (ii) The number x is a rational number. The number x is an irrational number.

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

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

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

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

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

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

Q.

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

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

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

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

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

Q. The negation of "3 + 7 = 10" is .

1. 3 = 10
2. 7 ≠ 10
3. 3 + 7 ≠ 10
4. 3 + 5 = 10

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

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

Q.

The statement $\sim (p\Rightarrow q)$ is equivalent to

1. $p\wedge \sim q$

2. $\sim p\wedge q$

3. $p\wedge q$

4. $\sim p\wedge \sim q$

Q.

Two statements p and q are given below

p: It is snowing
q: I am cold

The compound statement "It is snowing and it is not that I am cold" is given by

1. $p\wedge \sim q$

2. $\sim p\wedge q$

3. $p\wedge q$

4. $\sim p\vee \sim q$

Q. Identify the quantifier in the following statements and write the negation of the statements
(i) There exists a number which is equal to its square
(ii) For every real number $x,x$ is less than $x+1$
(iii) There exists a capital for every state in India

Q.

For any two statements p and q, the statement $\sim (p\vee q)\vee (\sim p\wedge q)$ is equivalent to

1. q

2. $\sim p$

3. $p$

4. $\sim q$

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

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

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

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

Q. Negation of ‘Azra is in class X or Diya is in class XII’ is ___.

1. Azra is not in class X or Diya is not in class XII
2. Azra is not in class X and Diya is not in class XII
3. Azra is in class X if and only if Diya is in class XII
4. If Azra is not in class X, then Diya is not in class XII

Q.

Negation of the statement 'if it rains, I shall go to school' is

1. It rains and I shall go to school

2. It rains and I shall not go to school

3. It does not rain and I shall go to school

4. It does not rain and I shall not go to school

Q. Check whether the following pair of statements is negation of each other. Give reasons for the answer. (i) x + y = y + x is true for every real numbers x and y . (ii) There exists real number x and y for which x + y = y + x .

Q.

From the given options, the truth values of p, q and r respectively for which $(p\wedge q)\vee (\sim r)$ has a truth value F are

1. T, T, T

2. T, F, F

3. F, F, F

4. F, F, T