Question

Let S be the set of all non-negative multiples of 4 (0,4,8,12 and so on). S is closed with respect to which ordinary operation?

Answer 1

addition

if you add two multiples of 4 then you will get a multiple of 4

for a sort of proof

let A and B be constants , therefore the sum of two multiples of 4 is given by S = 4A + 4B = 4 (A+B ) , which is indeed another multiple of 4

Answer 2

Also , 4A x 4B = 16AB = (4AB) x (4)

Answer 3

so it is also closed under multiplication

and since addition and subtraction are opposites and multiplication and divisions are opposites then it is closed under all operations