# NCERT Class 11-Math՚s: Chapter – 14 Mathematical Reasoning Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 2**:

Find the component statements of the following compound statements.

(i) Number is prime and odd.

(ii) Chennai is in India and is the capital of Tamil Nadu.

(iii) The number is divisible by , and .

(iv) Chandigarh is the capital of Haryana and U. P.

(v) is a rational number or an irrational number.

(vi) is less than every positive integer and every negative integer.

(vii) Plants use sunlight, water and carbon dioxide for photosynthesis.

(viii) Two lines in a plane either intersect at one point or they are parallel.

(ix) A rectangle is a quadrilateral or a sided polygon.

**Answer**:

(i) : Number is prime

: Number is odd

(ii) : Chennai is in India

: Chennai is capital of Tamil Nadu

(iii) is divisible by

is divisible by

is divisible by

(iv) Chandigarh is capital of Haryana

Chandigarh is the capital of U. P

(v) is a rational number

is an irrational number

(vi) is less than every positive integer

is less than every negative integer

(vii) plants use sunlight for photosynthesis

plants use water for photosynthesis

plants use carbon dioxide for photosynthesis

(viii) Two lines in a plane intersect at one point

two lines in a plane are parallel

(ix) a rectangle is a quadrilateral

a rectangle is a sided polygons.

**Question 3**:

Write the component statements of the following compound statements and check whether the compound statement is true or false.

(i) is divisible by or

(ii) is a multiple of and

(iii) All living things have two eyes and two legs.

(iv) is an even number and a prime number.

**Answer**:

(i) Compound statement is true and its component statements are:

is divisible by and is divisble by

(ii) Component statement is true and its component statements are:

is multiple of and is multiple of

(iii) Component statement is false and is component statements are

All living things have two eyes

All living things have two legs

(iv) Component statement is true and its component statements are:

is an number;

is a prime number

**Question 4**:

Write the negation of the following simple statements

(i) The number is prime.

(ii)

(iii) Violets are blue.

(iv) is a rational number.

(v) is not a prime number.

(vi) Every real number is an irrational number.

(vii) Cow has four legs.

(viii) A leap year has days.

(ix) All similar triangles are congruent.

(x) Area of a circle is same as the perimeter of the circle.

**Answer**:

(i) The number is not prime

(ii)

(iii) Violet are not blue

(iv) is not a rational number

(v) is a prime number

(vi) There exists a real number which is not an irrational number

(vii) Cow has not four legs

(viii) A leap year has not days

(ix) There exist similar triangles which are not congruent

(x) Area of a circle is not same as the perimeter of the circle