NCERT Class 11-Math's: Chapter –14 Mathematical Reasoning Part 12

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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 n2 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)

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