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Find the component statements of the following compound statements.

Question:

Find the component statements of the following compound statements.

(i) Number 7 is prime and odd.

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

(iii) The number 100 is divisible by 3, 11 and 5.

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

(vi) 0 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 5 – sided polygon.

Solution:

(i) Number 7 is prime and odd.

A compound statement is a combination of two statements (Components).

So, the components of the given statement “Number 7 is prime and odd” are,

p:Number 7 is prime.

q: Number 7 is odd.

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

A compound statement is a combination of two statements (Components).

So, the components of the given statement “Chennai is in India and is the capital of Tamil Nadu” are,

p: Chennai is in India.

q: Chennai is the capital of Tamil Nadu

(iii) The number 100 is divisible by 3, 11 and 5.

A compound statement is a combination of two statements (Components).

So, the components of the given statement “The number 100 is divisible by 3, 11 and 5”.

p: 100 is divisible by 3.

q: 100 is divisible by 11.

r: 100 is divisible by 5.

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

A compound statement is a combination of two statements (Components).

So, the components of the given statement “Chandigarh is the capital of Haryana and U.P.” are,

p: Chandigarh is the capital of Haryana and U.P

q: Chandigarh is the capital of U.P

(v) √7 is a rational number or an irrational number.

A compound statement is a combination of two statements (Components).

So, The components of the given statement √7is a rational number or an irrational number,

p: √7is a rational number.

q: √7 is an irrational

(vi) 0 is less than every positive integer and every negative integer.

A compound statement is a combination of two statements (Components).

So, the components of the given statement 0 is less than every positive integer and every negative integer are

p: 0 is less than every positive integer

q: 0 is less than every negative integer.

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

A compound statement is a combination of two statements (Components).

So, the components of the given statement “Plants use sunlight, water and carbon dioxide for photosynthesis” are

p: Plants use sunlight for photosynthesis

q: Plants use water for photosynthesis

r: Plants use carbon dioxide for photosynthesis

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

A compound statement is a combination of two statements (Components).

So, the components of the given statement Two lines in a plane either intersect at one point or they are parallel “are

p: Two lines in a plane intersect at one point.

q: Two lines in a plane are parallel.

(ix) A rectangle is a quadrilateral or a 5 – sided polygon.

A compound statement is a combination of two statements (Components).

So, the components of the given statement “A rectangle is a quadrilateral or a 5 – sided polygon” are

p: A rectangle is a quadrilateral

q: A rectangle is a 5 – sided polygon.

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