Question

Consider the following statements: For non empty sets $A,B$and $C$.

$$\begin{gathered} 1.A–(B–C)=(A–B)\cup C \\ 2.A–(B\cup C)=(A–B)–C \end{gathered}$$

Which of the statements given 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 B

$2$only

The explanation for the correct option :

Step 1. Draw the venn diagram :

Let there be three non-empty sets $A,BandC$ inside a universal set $U$ .

We have marked $8$ regions as $a,b,c,d,e,f,g,h.$

Step 2. Check Statements :

Statement $1:A–(B–C)=(A–B)\cup C$

LHS represents region $a$ , RHS represents $a,d,g.$

Hence, this is not correct.

Statement $2:A–(B\cup C)=(A–B)–C$

LHS represents, region $a$ RHS also represents $a$ .

Thus, only statement $2$ is correct.

Hence, the correct option is B.