subset problem: Determine if A is a subset of B, B is a subset of A or A=B

[Lauriecal13]

Determine if A is a subset of B, B is a subset of A or A=B
A:={x∈Z | x is a multiple of 3},
B:={x∈Z | x=21+3y for some y∈Z}

 

[mmm4444bot]

Determine if A is a subset of B, B is a subset of A or A=B

A:={x∈Z | x is a multiple of 3}

B:={x∈Z | x = 21 + 3y for some y∈Z}

If we sum two multiples of 3, do we get another multiple of 3?

If you're not sure how my question pertains, then try listing out some elements of each set and compare the patterns.

If you need more help, please explain what you tried or thought about, so far. Thanks :cool:

 

[stapel]

Determine if A is a subset of B, if B is a subset of A, or if A = B, given the following two set definitions:

. . . . .A = {x∈Z | x is a multiple of 3}

. . . . .B = {x∈Z | x = 21 + 3y for some y∈Z}

You know that all elements of A are of the form 3m, for some integer m, because they are all multiples of 3.

Is there any way to express elements of B as multiples of 3? In particular, is there any way to equate the members of the two sets?