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

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions.

- anonymous

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

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

hey, how's it going?

- anonymous

hi there I am just cracking my head on this proof

- anonymous

I started but am stuck

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

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

- anonymous

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

- anonymous

yes

- anonymous

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

- anonymous

yeah

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

right I understand that so far

- anonymous

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

- anonymous

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

- anonymous

yes

- anonymous

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.

- anonymous

hey, you still there?

Looking for something else?

Not the answer you are looking for? Search for more explanations.