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If U = {2, 3, 5, 7, 9} is the Universal Set and a = {3, 7}, B = {2, 5, 7, 9}, Then Prove That: ( a ∩ B ) ′ = a ′ B ′ . - Mathematics

If U = {2, 3, 5, 7, 9} is the universal set and A = {3, 7}, B = {2, 5, 7, 9}, then prove that:

\[\left( A \cap B \right)' = A'B' .\]

 

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Solution

Given:
U = {2, 3, 5, 7, 9}
A = {3, 7}
B = {2, 5, 7, 9} 

To prove : 

\[\left( A \cap B \right)' = A' \cup B'\] 

Proof :

 LHS: 

\[(A \cap B) = {7}\]
\[(A \cap B)' = {2, 3, 5, 9}\]

RHS: 

\[A' = {2, 5, 9}\]
\[B' = {3}\]
\[A' \cup B' = {2, 3, 5, 9}\]

LHS = RHS

∴ \[\left( A \cap B \right)' = A' \cup B'\]

Concept: Universal Set
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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 1 Sets
Exercise 1.6 | Q 3.2 | Page 27
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