# NCERT Class 11-Math՚S: Chapter – 14 Mathematical Reasoning Part 12 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 16**:

Using contrapositive method prove that if is an even integer, then *n* is also an even integers.

**Answer**:

Let us Assume

is an even integer.

is not an even integer

is also an even integer

is not an even integer.

Since, In the contrapositive, a conditional statement is logically equivalent to its contrapositive.

Therefore,

If n is not an even integer then n^{2} is not an even integer.

Hence, is true is true.

## Objective Type Questions

### Choose the Correct Answer Out of the Four Options Given Against Each of the Exercises 17 to 36 (M. C. Q.)

**Question 17**:

Which of the following is a statement.

(A) is a real number.

(B) Switch off the fan.

(C) is a natural number.

(D) Let me go.

**Answer: (C)**

**Question 18**:

Which of the following is not a statement

(A) Smoking is injurious to health.

(B)

(C) is the only even prime number.

(D) Come here.

**Answer: (D)**

**Question 19**:

The connective in the statement “” is

(A) And

(B) Or

(C)

(D)

**Answer: (B)**

**Question 20**:

The connective in the statement

“Earth revolves round the Sun and Moon is a satellite of earth” is

(A) Or

(B) Earth

(C) Sun

(D) And

**Answer: (D)**

**Question 21**:

The negation of the statement

“A circle is an ellipse” is

(A) An ellipse is a circle.

(B) An ellipse is not a circle.

(C) A circle is not an ellipse.

(D) A circle is an ellipse.

**Answer: (C)**

**Question 22**:

The negation of the statement

“A circle is an ellipse” is

(A) An ellipse is a circle.

(B) An ellipse is not a circle.

(C) A circle is not an ellipse.

(D) A circle is an ellipse.

**Answer: (B)**

**Question 23**:

The negation of the statement

“72 is divisible by 2 and 3” is

(A) 72 is not divisible by 2 or 72 is not divisible by 3.

(B) 72 is not divisible by 2 and 72 is not divisible by 3.

(C) 72 is divisible by 2 and 72 is not divisible by 3.

(D) 72 is not divisible by 2 and 72 is divisible by 3.

**Answer: (A)**