Question

Let A,B,C are subsets of set X. Then consider the validity of the following set theoretic statement:

• A. $A\cup(B/C)=(A\cup B)/(A\cup C)$
• B. $(A/B)/C=A/(B\cup C)$
• C. $(A\cup B)=A/B$
• D. $A/B=B/C$

Answer 1

Answer: (B)

$(A/B)/C=A/(B\cup C)$

Answer 2

The correct answer is option (B): $(A/B)/C=A/(B\cup C)$

We know that if $A\cup B=A\cup C$ and $A\cap B=A\cap C$, then B=C which gives A$\subset$C

Hence, (A /B)/C =A /(B ∪ C)