Search 80,000+ tutors
FIND TUTORS

Elementry Topics 2

Containment and Equality

If A and B are sets, then A is said to be contained in B iff (if and only if) every element of A is contained in B. So A⊆B means that A is a subset of B.
Example:
All squares ⊆ all rectangles
All right triangles ⊆ all triangles

Important! This implies the idea of forwards and backwards logic: If Joe has three million dollars, he is a millionaire. If Joe is a millionaire it doesn’t necessarily mean he has three million dollars, he could have one million dollars and still be a millionaire. Likewise, all squares are rectangles but not all rectangles are squares.

A=B iff A⊆B and B⊆A

Example:
{x:x^2=4}={-2,2}
{x:x^2<4}={x:-2<x<2}

$20p/h

Joshua M.

I Do More Than Just Math and I'll Even Throw in a Laugh!

5+ hours
if (isMyPost) { }