- #1

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## Homework Statement

Prove the following for a given universe U

A⊆B if and only if A∩(B compliment) = ∅

## Homework Equations

## The Attempt at a Solution

Assume A,B, (B compliment) are not ∅

if A∩(B compliment) = ∅, x∈A ∨ x∈ (B compliment), but not both

If x∈A ∧ x∉(B compliment), then x∈B , because if they are in the same U and A∩(B compliment) = ∅ then A∩B must have a common element.

Also A⊆B because if A was outside of B, then A∩(B compliment) ≠ ∅