Question

Let A and B be any two sets. Show that:Show that (A' UB)' (BUA)' = $​
A. True
B. False

Answer 1

To show that (A' ∪ B)' ∤ (B ∪ A)' is true, we can simplify the expression step by step using De Morgan's Law.

Step-by-step explanation:

In this case, we need to simplify the given expression (A' ∪ B)' ∤ (B ∪ A)'.

Using De Morgan's Law, we can rewrite (A' ∪ B)' as A'' ∩ B'.

Since A'' is equivalent to A, and A ∩ B' is equivalent to A - B, the expression becomes A - B ∤ (B ∪ A)'.

Next, we use De Morgan's Law again to rewrite (B ∪ A)' as B' ∩ A'.

Finally, we have A - B ∤ B' ∩ A'.

Since B' ∩ A' is equivalent to (A ∪ B)', the expression becomes A - B ∤ (A ∪ B)'.

Therefore, the expression (A' ∪ B)' ∤ (B ∪ A)' is equal to A - B ∤ (A ∪ B)'. Hence, the answer is True.