# Let a = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the Following Identities: a ∪ ( B ∩ C ) = ( a ∪ B ) ∩ ( a ∪ C ) - Mathematics

Let A = {1, 2, 4, 5} B = {2, 3, 5, 6} C = {4, 5, 6, 7}. Verify the following identities:

$A \cup \left( B \cap C \right) = \left( A \cup B \right) \cap \left( A \cup C \right)$

#### Solution

Given:
A = {1, 2, 4, 5}, B = {2, 3, 5, 6} and C = {4, 5, 6, 7}
We have to verify the following identities:

$A \cup \left( B \cap C \right) = \left( A \cup B \right) \cap \left( A \cup C \right)$

LHS

LaTeX

$(B \cap C) = {5, 6}$
$A \cup (B \cap C) = {1, 2, 4, 5, 6}$
RHS
$\left( A \cup B \right) = {1, 2, 3, 4, 5, 6}$
$\left( A \cup C \right) = {1, 2, 4, 5, 6, 7}$
$\left( A \cup B \right) \cap \left( A \cup C \right) = {1, 2, 4, 5, 6}$
LHS = RHS
∴ $A \cup \left( B \cap C \right) = \left( A \cup B \right) \cap \left( A \cup C \right)$
Concept: Operations on Sets - Union Set
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.6 | Q 2.1 | Page 27