Let x, y, and z be integers. Prove that
(a) if x and y are even, then x + y is even.
(b) if x is even, then xy is even.
(c) if x and y are even, then xy is divisible by 4.
(d) if x and y are even, then 3x − 5y is even.
(e) if x and y are odd, then x + y is even.
(f ) if x and y are odd, then 3x − 5y is even.
(g) if x and y are odd, then xy is odd.
(h) if x is even and y is odd, then x + y is odd.
(i) if exactly one of x, y, and z is even, then the sum of x, y, and z is even.
(j) if exactly one of x, y, and z is odd, then xy + yz is even.
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