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

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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

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