Check whether the following statements are true and false
(i) 101 is a prime number or a composite number
(ii) A hexagon is 6 sided polygon or rectangle
(iii) `sqrt(157)` is a rational number or an interger
(iv) Two lines intersect at a point or are parellel

Explanation

Here ''OR'' is exclusive and component statements are
p : 101 is a prime number (True)
q : 101 is a compositive number (False)
Here, p is true and q is false so compound statement is true
(ii) Here "OR" is exclusive and component statements are
p : A hexagonal is 6 sided polygon. (True)
q : hexagonal is a rectangle. (False)
Here, one component statement is true, so compound statement is true.
(iii) Here inclusive "OR" is used, and component statements are
p : `sqrt(157)` is a rational number. (False)
q `sqrt(157)` is a integer. (False)
Here both p and q are false, so compound statement is false.
(iv). Here exclusive "OR" is used and the compound statements are
p : Two llnes intersect at a point. (True)
r : Two lines are parallel. (True)
Here when p is true r is false and when r is true p is false . So the compound statement is true