Question

Consider the following:
1. $A\cup (B\cap C)=(A\cap B)\cup (A\cap C)$
2. $A\cap (B\cup C)=(A\cup B)\cap (A\cup C)$
Which of the above is/are correct?

• A. 1 only
• B. 2 only
• C. Both 1 and 2
• D. Neither 1 nor 2

Answer 1

The correct option is D Neither 1 nor 2

Figure $1$ represents $A\cup (B\cap C)$ and figure $2$ represents $(A\cap B)\cup (A\cap C)$. We ca see both of them are not equal.

Figure $3$ represents $A\cap (B\cup C)$ and figure $4$ represents $(A\cup B)\cap (A\cup C)$. We can see both of them are not equal.

So, both the equations are incorrect.