Prove or disprove the statement by mathematical induction

Question

For ∀ a, b ∈ Z^+ ^ a>b → b^a > a^b

Answer 1

The statement is false....

a=2 > 1=b for a=2 and b=1 both positive integers...

b^a = 1^2 =1 while a^b = 2^1 = 2

in fact for b=1 and any positive integer a>1=b,

b^a = 1^a = 1 while a^b = a^1 = a > 1 = b^a