Q68 of 142 Page 88

State whether the statements are true (T) or false (F).
If x and y are integers such that x²>y², then x³>y³.

Given: integer x and y

For an integer x and y as (-1) and (-2) respectively.

x²>y²⇒ (-2)² > (-1)² = 4 > 1 (true)

and x³>y³⇒ (-2)³ > (-1)³ = -8 > -1 (not true)

as -8 < -1

Hence, the given statement is false.

State whether the statements are true (T) or false (F).

All numbers of a Pythagorean triplet are odd.

State whether the statements are true (T) or false (F).

For an integer a, a³ is always greater than a².

State whether the statements are true (T) or false (F).

If x and y be natural numbers. If x divides y, then x³ divides y³.

State whether the statements are true (T) or false (F).

If a² ends in 5, then a³ ends in 25.

State whether the statements are true (T) or false (F).If x and y are integers such that x2>y2, then x3>y3.