(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Prove A contained B iff A n B = A

2. Relevant equations

none

3. The attempt at a solution

I tried to do the questions but im just not sure if i did it right. id appreciate if you can check my work and let me know what changes i have to make. thanks

the symbol "n" means "intersect"

U for Union

(=>) Assume A contained B

Let x is an element of A, since A n A = A, x is an element of A and x is an element of B

Case 1: x is an element of A: Since A contained B, x is an element of B so

x is an element of A n B

Case 2: x is an element of B: If x is an element of B then

x is an element of (A n B)

Hence x is an element of A n B

This shows A contained A n B

(<=) Assume A n B = A then

A’=A’UA

= A’ U (A n B)

=(A’UA) n (A’U B)

= empty set n A’ U B

= A’ U B

Hence

Universe = A’ U B

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