Let A= 1,2,4,5 , B= 2,3,5,6 , C= 4,5,6,7 verify the following ide… - Vidyadip

Question

Let $A=\{1,2,4,5\}, B=\{2,3,5,6\}, C=\{4,5,6,7\}$ verify the following identity:
$A \cup(B \cap C)=[(A \cup B) \cap(A \cap C)]$

✓

Answer

L.H.S. $=\mathrm{A} \cup(\mathrm{B} \cap \mathrm{C})$
$=\{1,2,4,5\} \cup[\{2,3,5,6\} \cap\{4,5,6,7\}]$
$=\{1,2,4,5\} \cup\{5,6\}$
$=\{1,2,4,5,6\}$
R.H.S. $=(A \cup B) \cap(A \cup C)$
$=[\{1,2,4,5\} \cup\{2,3,5,6\}] \cap[\{1,2,4,5\} \cup\{4,5,6,7\}]$
$=\{1,2,3,4,5,6\} \cap\{1,2,4,5,6,7\}$
$=\{1,2,4,5,6\}$
$\therefore$ L.H.S. $=$ R.H.S. Hence verified.

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