(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?

Printable View

- 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 "$\displaystyle X\subseteq Y$" 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, "$\displaystyle A\cap B$" is defined as the set of all x such that x is in A and x is in B. If $\displaystyle x\in A\cap B$ then $\displaystyle x\in A$. Now, you need to show "if $\displaystyle x\in A$ then $\displaystyle x\in A\cup B$". So, what is the

**definition**of "$\displaystyle A \cup B$"?