Question

Find the component statements for the following compound statement.


(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 $3,11\text{and}5$.

(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 they are parallel

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

Answer 1

(i)

Compound statement: "Number $7$ is prime and odd".
Component statements of given compound statement are:

p : Number $7$ is prime.
q : Number $7$ is odd.

(ii)

Compound statement: "Chennai is in India and is the capital of Tamil Nadu".

Component statements of given compound statement are:

p : Chennai is in India.
q : Chennai is the capital of Tamil Nadu.

(iii)

Compound statement: "The number $100$ is divisible by $3,11\text{and}5$".

Component statements of given compound statement are:

p : The number 100 is divisible by $3$.
q : The number 100 is divisible by $11$.
r : The number 100 is divisible by $5$.

(iv)

Compound statement: "Chandigarh is the capital of Haryana and U.P".
Component statements of given compound statement are:

p : Chandigarh is capital of Haryana.
q : Chandigarh is capital of U.P.


(v)

Compound statement: "$\sqrt{7}$ is a rational number or an irrational number".

Component statements of given compound statement are:
p : $\sqrt{7}$ is a rational number.
q : $\sqrt{7}$ is an irrational number.


(vi)

Compound statement: "$0$ is less than every positive and every negative integer".
Component statements of given compound statement are:
p : 0 is less than every positive integer.
q : 0 is less than every negative integer.

(vii)

Compound statement: "Plants use sunlight, water and carbon dioxide for photosynthesis"

Component statements of given compound statement are:
p : Plants use sunlight for photosynthesis.
q : Plants use water for photosynthesis.
r : Plants use carbon dioxide for photosynthesis.


(viii)

Compound statement: "Two lines in a plane either intersect at one point or they are parallel".
Component statements of given compound statement are:
p : Two lines in a plane intersect at one point.
q : Two lines in a plane are parallel.


(ix)

Compound statement: "A rectangle is a quadrilateral or a 5-sided polygon".

Component statements of given compound statement are:
p : A rectangle is a quadrilateral.
q : A rectangle is a 5-sided polygon.