Thread: Another sets prove

By using the set algebra , prove that , for any sets A and B
A u ( A' n B ) = A u B

Deduce , or using set algebra , show that

A u ( A' n B ) u [A' n (A u B') n {B u (B' n C}] = A u B u C

The question test the distributive laws.

A u ( A' n B ) = A u B
from L.H.S : A u ( A' n B )
= ( A U A' ) n ( A u B )
= S n ( A u B )
= A u B ( proven )

You should be able to solve the second part using the law or the procedure listed above

Originally Posted by mathaddict

By using the set algebra , prove that , for any sets A and B
A u ( A' n B ) = A u B

Deduce , or using set algebra , show that

A u ( A' n B ) u [A' n (A u B') n {B u (B' n C}] = A u B u C

Originally Posted by mathaddict

Deduce , or using set algebra , show that

A u ( A' n B ) u [A' n (A u B') n {B u (B' n C}] = A u B u C

I tried this one but i couldn't get the prove . Can someone pls spot my mistake .

My working :

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

wondering , where is the A .

Hello mathaddict

Originally Posted by mathaddict

I tried this one but i couldn't get the prove . Can someone pls spot my mistake .

My working :

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

wondering , where is the A .

Here's a proof - there might be a quicker one:



, using the first result twice

, Distributive Law

, Complement Law

, Identity Law

, De Morgan's Law

, Distributive Law

, Complement Law

, Identity Law, Associative Law

, Idempotent Law

Grandad