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Find the component statements of the fol...

Find the component statements of the following compound statements and check whether they are true or false.
(i) `sqrt(5)` is a rational number or an irrational number.
(ii) Chandigarh is the capital of hartyana and punjab.
(iii) a multiple of 2,4 and 6 is 16.
(iv) a sequare is a quadrilateral and all 4 sides of it are equal.
(v) all integers are positive or negative.

Text Solution

Verified by Experts

(i) component statements are :
`p :sqrt(5)` is a rational number.`q : sqrt(5)` is an irrational number. Here p is false and q is true, the connecting word is 'or'
(ii) component statements are :
`p :` Chandigarh is the capital of haryana. `q : ` Changdigarh is the capital of punjab. here both statements are true. the connecting word is 'and' .
(iii) component statements are :
`p:` a multiple of 2 is 16.
`q:` a multiple of 4 is 16. r : a multiple of 6 is 16. here p and q are true and r is false. the connecting word is 'and'
(iv) component statements are :
p : a square is a quardrilateral. q: all sides of a square are equal. here both statements are true. the connecting word is 'and'.
(v) component statements are.
p: all integers are postive :
`q:` all integers are negative. here both statements are false. the connecting word is 'or'
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