State for each of the following statements whether it is true or false :

(a) If (x - a)(x - b) < 0, then x < a and x < b.

(b) If a < 0 and b < 0, then (a + b)² > 0.

(c) If a and b are any two integers such that a > b, then a² > b².

(d) If p = q + 2, then p > q.

(e) If a and b are two negative integers such that a < b, then $\dfrac{1}{a} \lt \dfrac{1}{b}$

(a) False
Reason — If x < a and x < b, then (x - a)(x - b) will be greater than 0 as multiplication of two negative number generates a positive number.

(b) True
Reason — If a < 0 and b < 0, then (a + b) will be a negative number and square of any negative number is greater than 0, so (a + b)² is greater than 0.

(c) False
Reason — If a > b, then a² > b² is true only if a and b are positive numbers.

(d) True
Reason — If a positive number is added to any number (suppose x), then resultant number is greater than x.

(e) False
Reason — If, a < b and both are two negative integers then on recripocating the numbers the sign will be reversed, so $\dfrac{1}{a} \gt \dfrac{1}{b}$.