Question

Prove: A is a subset of B iff A-B= empty set

Answer 1

hey, how's it going?

Answer 2

hi there I am just cracking my head on this proof

Answer 3

I started but am stuck

Answer 4

hmm, i'm not the best at formal proofs, but let's see

Answer 5

A is a subset of B means that every element of A is an element of B

Answer 6

yes

Answer 7

then A-B is the set of elements in A that don't belong to set B

Answer 8

yeah

Answer 9

but since A is a subset of B, we know that every element of A is an element of B, so that means that there are no elements in A that don't belong to set B

Answer 10

that's a little confusing can you explain that again?

Answer 11

we want to know what A-B is, or the set of elements in A that don't belong to B

Answer 12

we started with A is a subset of B, which means that every element of A is an element of B

Answer 13

right I understand that so far

Answer 14

so for any element in A, we know that it is also in B

Answer 15

so for any element in A, we know that it is also in B

Answer 16

yes

Answer 17

so we are considering A-B, or the set of elements in A that don't belong to B. Let's assume element x is in A-B. that means that x is in A, and x is not in B. but we know that can't be true because for any element in A, we know it is in B. so x cannot exist! therefore A-B is the empty set.

Answer 18

hey, you still there?