1. ## [SOLVED] Proofs

Prove the following:

1. For all set A and B, A c A U B

2. For all sets A and B, A U B c A ∩ B

3. For all set A and B, A - B = A ∩ B

4. For all sets A and B, if A c B, then B c A

5. For all sets A, B, and C, A-(B U C) = (A - B) ∩ (A - C)

2. Originally Posted by akeem
Prove the following:

1. For all set A and B, A c A U B
For all x in A x is of necessity in (A union B), by definition of union.

You may worry that this does not work if A is the null set, but as the
null set is a subset of every set the result still holds (and you don't really
need to so worry).

RonL

3. Hello, akeem!

Are there typos?
. . Most of these are not true . . .

Prove the following for all sets $\displaystyle A,\,B,\,C:$

$\displaystyle 1.\;\;A \:\subseteq \:A \cup B$ . True

$\displaystyle 2.\;\;A \cup B \;\subseteq \; A \cap B$ . Not true

$\displaystyle 3.\;\;A - B \:= \:A \cap B$ . Not true

$\displaystyle 4.\;\;\text{If }A \subseteq B,\text{ then }B \subseteq A$ . Not true

$\displaystyle 5.\;\;A - (B \cup C) \:= \:(A - B) \cap(A - C)$ . True