Question

Math proof. Suppose that A\B are disjoint from C and x is in the element of A. Prove that if x is in the element of C then x is in the element of B.

Answer 1

where are you stuck?

Answer 2

if x is in C what can you say about x's relationship with A\B?

Answer 3

I'm stuck at the very beginning.. So I have my givens: x is not in (A\B n C) and x is in A. My goal: x is in C which implies that x is in B.

Answer 4

Which I can further imply from my givens that x is not in B and x is not in C. Right?

Answer 5

if x is in C then x is not in A\B so x is in (A\B)'

Answer 6

\[A\backslash B=A\cap B'\]

Answer 7

so \[(A\backslash B)'=A'\cup B\]

Answer 8

so \(x\in A\) and \(x\in A'\cup B\)

ie

\[x\in A\cap(A'\cup B)=A\cap B\subseteq B\]

Answer 9

Does A' mean its not A?

Answer 10

the complement of A

\[\overline{A},A',A^{c}\]

whatever notation you use.

Answer 11

HAH, okay gotcha.

Answer 12

good :)