# Math Help - im pretty sure this is true

1. ## im pretty sure this is true

(A and B) U (A - C) = A -(C - B)

(A and B) U (A - C) = A -(C - B)
HI

We will start from the LHS .

(A n B) u (A-C)

(A n B) u (A n C')

A n (B u C') .... distributive

A n (B' n C)' ..... de morgan

A n (C n B')' .... associative

A - (C - B)

3. can you explain de Morgan's law

can you explain de Morgan's law
$\left[\bigcup_{i=1}^{n} U_i \right]^c=\bigcap_{i=1}^{n}U_i^c$ where $^c$ denotes the complement. An obvious corrolary of this is that $\left[\bigcap_{i=1}^{n}U_i\right]^c=\left[\bigcap_{i=1}^{n}\left(U_i^c\right)^c\right]^c=\left[\left[\bigcup_{i=1}^{n}U_i^c\right]^c\right]^c=\bigcup_{i=1}^{n}U_i^c$.

can you explain de Morgan's law
De morgan's law states that

(A u B)'=A' n B'

(A n B)'=A' u B'