Question

Consider the following relations

$1.A-B=A-(A\cap B)$

$2.A=(A\cap B)\cup (A-B)$

$3.A-(B\cup C)=(A-B)\cup (A-C)$

Which of these is/are correct?

• A. $1$ and $3$
• B. $2$ only
• C. $2$ and $3$
• D. $1$ and $2$

Answer 1

The correct option is D

$1$ and $2$

The explanation for the correct option:

Finding which option is correct.

$1.A-B=A-(A\cap B)$is correct as it is the difference law

$2.A=(A\cap B)\cup (A-B)$ is correct since

$A=(A\cap B)\cup (A-B)=\left(A\cap B\right)\cup \left(A-\left(A\cap B\right)\right)=A$

$3.A-(B\cup C)=(A-B)\cup (A-C)$is incorrect by distribution law $A-(B\cup C)=(A-B)\cap (A-C)$

Thus, $1$and $2$and correct.

Hence, the correct option is (D).