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  • Show that for any sets A and B, A = ( A ∩ B ) ∪ ( A – B ) and A ∪ ( B – A ) = ( A ∪ B )

Q8. Show that for any sets A and B,

A = ( A \cap B ) \cup ( A – B ) and A \cup ( B – A ) = ( A \cup B )

Answers (1)

best_answer

A = ( A \cap B ) \cup ( A – B )

L.H.S = A = Red coloured area

R.H.S =  ( A \cap B ) \cup ( A – B )

( A \cap B ) = green coloured

( A – B ) =  yellow coloured

( A \cap B ) \cup ( A – B ) = coloured part

Hence, L.H.S = R.H.S = Coloured part

 

A \cup ( B – A ) = ( A \cup B )

A = sky blue coloured

( B – A )=pink coloured 

L.H.S = A \cup ( B – A ) = sky blue coloured + pink coloured 

R.H.S = ( A \cup B ) = brown coloured part

L.H.S = R.H.S = Coloured part

 

 

 

 

 

 

 

Posted by

seema garhwal

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