NDA 2019 Maths · Mathematics · Sets, Relations and Functions · medium

If A⊂ B, then B'⊂ A' for subsets of a universal set U. 2. (A∪ B)-C=(A-C)∪(B-C) for any sets A,B,C.

Single correct option

Consider the following statements:
1. If

A\subset B

, then

B'\subset A'

for subsets of a universal set

U

.
2.

(A\cup B)-C=(A-C)\cup(B-C)

for any sets

A,B,C

.
Which of the statements given above is/are correct?

Show answer and solution

Answer: (C) Both 1 and 2

Statement 1: if

x\notin B

then

x\notin A

(since

A\subset B

), so

B'\subset A'

; it is true. Statement 2: an element is in

(A\cup B)-C

exactly when it is in

A

B

and not in

C

, which is the same as being in

A-C

or in

B-C

. Both are correct, as Venn diagrams also confirm.

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake