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)
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)
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