Show that A ∩ B = A ∩ C need not imply B = C

Solution:

In set theory, for any two sets A and B, the intersection is defined as the set of all the elements in set A that are also present in set B.

We use the symbol '∩' that denotes 'intersection of'.

Let A = {0, 1}, B = {0, 2, 3} and C = {0, 4, 5}

Accordingly,

A ∩ B = {0} and A ∩ C = {0}

Here,

A ∩ B = A ∩ C = {0}

However,

B ≠ C [Since 2 ∈ B and 2 ∉ C]

NCERT Solutions Class 11 Maths Chapter 1 Exercise ME Question 10

Show that A ∩ B = A ∩ C need not imply B = C

Summary:

Three sets are given. We have proved that A ∩ B = A ∩ C = {0}