Learn Show That A B A C Need Not Imply B C

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# 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}

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