NDA 2016 Maths · Mathematics · Sets, Relations and Functions · medium

Let A, B and C be sets. 1. A∩(B∪ C)=(A∩ B)∪ C. 2. (A∪ B)'=A'∪ B'.

Single correct option

Let

A

B

and

C

be sets. Consider the following statements:
1.

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

.
2.

(A\cup B)'=A'\cup B'

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

Show answer and solution

Answer: (D) Neither 1 nor 2

The correct distributive law is

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

; the statement leaves out

A

on the right, so it fails (take

C

outside

A

). De Morgan's law gives

(A\cup B)'=A'\cap B'

, not union. Both are false.

Original question written in the NDA 2016 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