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in Mathematics by kratos

Find the component statements of the following compound statements and check whether they are true or false.

(i) Numbers 3 is prime or it is odd

(ii) All integers are positive or negative

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

(iv) A square is a quadrilateral and its four sides equal

(v) All prime numbers are either even or odd

(vi) Chandigarh is the capital of Haryana and P.

(vii) 24 is a multiple of 2, 4 and 8

1 Answer

+4 votes
by kratos
 
Best answer

(i) The component statements are

p : number 3 is prime

q : number 3 is odd

Both p and q are true

(ii) The component statements are

p : all integers are positive

q : all integers are negative

Both p and q are false

(iii) The component statements are

p : 100 is divisible by 3 (false)

q : 100 is divisible by 11 (false)

r : 100 is divisible by 5 (true)

(iv) The component statements are

p : a square is a quadrilateral

q : a square has all its sides equal

Both p and q are true

(v) The component statements are

p : all prime numbers are even

q : all prime numbers are odd

Both p and q are false

(vi) The component statements are

p : Chandigarh is the capital of Haryana (True)

q : Chandigarh is the capital of U.P.(False)

(vii) The component statements are

p : 24 is a multiple of 2 (True)

q : 24 is a multiple of 4 (True)

r : 24 is a multiple of 8 (True)

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