(A intersect B) is contained in A is contained in (A union B)

I know I have to show containment both ways, meaning

(A intersect B) is contained in A

A is contained in (A union B)

Can you help me get started?

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- Sep 1st 2012, 10:06 AMlovesmathProving Intersections and Unions
(A intersect B) is contained in A is contained in (A union B)

I know I have to show containment both ways, meaning

(A intersect B) is contained in A

A is contained in (A union B)

Can you help me get started? - Sep 1st 2012, 10:32 AMemakarovRe: Proving Intersections and Unions
To prove that X is contained in Y, show that every element of X is an element of Y. Use the definitions of union and intersection.

- Sep 1st 2012, 10:36 AMPlatoRe: Proving Intersections and Unions
- Sep 1st 2012, 10:50 AMHallsofIvyRe: Proving Intersections and Unions
The way you prove " " is to start "if x is in X" then use the definitions of X and Y to show "then x is in Y". As Plato said, " " is defined as the set of all x such that x is in A and x is in B. If then . Now, you need to show "if then ". So, what is the

**definition**of " "?