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  • Find the component statements of the following compound statements. i) Number 7 is prime and odd.

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.

v) \sqrt{7}  is a rational number or an irrational number.

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 are parallel.

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

 

Answers (1)

i) Concept:

A compound statement is defined as a combination of two statements or components. Here the components of the given statement “number 7 is prime and odd, will be:

p: Number 7 is prime, &

q: Number 7 is odd

ii) Concept:

A compound statement is defined as a combination of two statements or components. Here the components of the given statement “Chennai is in India and is the capital of Tamil Nadu”, will be:

p: Chennai is in India

q: Chennai is the capital of Tamil Nadu

iii) Concept:

A compound statement is defined as a combination of two statements or components. Here the components of the given statement “the number 100 is divisible by 3, 11 & 5”, will be:

p: 100 is divisible by 3

q: 100 is divisible by 11 &

r: 100 is divisible by 5

iv) Concept:

A compound statement is defined as a combination of two statements or components. Here the components of the given statement “Chandigarh is the capital of Haryana and U.P.”, will be:

p: Chandigarh is the capital of Haryana &

q: Chandigarh is the capital of U.P.

v) Concept:

A compound statement is defined as a combination of two statements or components. Here, the components of the given statement \sqrt{7}  is a rational number or an irrational number”, will be:

p: \sqrt{7} is a rational number, &

q: \sqrt{7} is an irrational number

vi) Concept:

A compound statement is defined as a combination of two statements or components.Here the components of the given statement “0 is less than every positive integer and every negative integer”, will be –

p: 0 is less than every positive integer, &

q: 0 is less than every negative integer

vii) Concept:

A compound statement is defined as a combination of two statements or components. Here the components of the given statement “Plants use sunlight, water and carbon dioxide for photosynthesis”, will be –

p: Plants use sunlight for photosynthesis

q: Plants use water for photosynthesis &

r: Plants use carbon dioxide for photosynthesis

viii) Concept:

A compound statement is defined as a combination of two statements or components. Here the components of the given statement “two lines in a plane either intersect at one point or they are parallel”, will be –

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

q: Two lines in a plane are parallel

ix) Concept:

A compound statement is defined as a combination of two statements or components. Here the components of the given statement “A rectangle is a quadrilateral or a 5 – sided polygon”, will be –

p: A rectangle is a quadrilateral

q: A rectangle is a 5 – sided polygon.

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