Answer to Question #278426 in Discrete Mathematics for wafrets

Question

If x and y are not both even numbers, then neither the square of x and y is odd, nor the cube of x and y is even

Answer 1

Answer: false

for example, if x is even and y is odd numbers, then:

$x=2k_1$

$y=2k_2+1$

where k₁, k₂ = 0,1,2,3,...

$(x+y)^2=(2k_1+2k_2+1)^2$ is odd