Question

for any two sets A and B prove by using properties of sets that (A⋂B)⋃(A-B)=A

Answer 1

Set is a collection of well defined object or data

Example :-

• The vowels in the english alphabet

• Prime Factor of 210

• The collection of all boys in your class

_______________

$\underline{ \large{ \bold{Let \: , \: \: }}}$

$\to \bold{A = ( \: 1, 2 \: )\: } \\ \to \bold{B = ( \: 1, 3 , 4 \: ) \: }$

$\large{ \bold{\fbox{ \fbox{To \: Prove :- \: }}}}$

$\to \: \bold{( \: A \: ⋂ \: B \: ) \: ⋃ \: ( \: A - B \: ) = A \: }$

$\large\bold{ \fbox{ \fbox{Solution :- \: }}}$

$\to \bold{( \: A \: ⋂ \: B \: ) = ( \: 1 , 2 \: ) \: ⋂ \: ( \: 1, 3 , 4 \: ) = ( \: 1 \: ) \: } \\ \\ \to \bold{( \: A - B \: ) = ( \: 1 , 2 \: ) - ( \: 1 , 3 , 4 \: ) = ( \: 2 \: ) \: }$

$\underline{ \bold{ \large{So \: , \: \: }}}$

$\to \bold{ {( \: A \: ⋂ \: B \: ) \: ⋃ \: ( \: A - B \: ) \: }} \\ \\ \to\bold{ ( \: 1 \: ) \: ⋃ \: ( \: 2 \: ) } \\ \\ \to\bold{</p><p>( \: 1, 2 \: ) } \: = \bold{ \: A \: }$