Question

2. If A={1,4},B={2,3},C={3,5} then find i)AX(B UC) ii) (AXB)U(AXC) iii) AX(B∩C) iv)(AXB) ∩(AXC)

Answer 1

Explanation:

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Answer 2

Answer:

i : { ( 1 , 2 ) , ( 1 , 3 ) , ( 1 , 5 ) , ( 4 , 2 ) , ( 4 , 3 ) , ( 4 , 5 ) }

ii : { ( 1 , 2 ) , ( 1 , 3 ) , ( 4 , 2 ) , ( 4 , 3 ) , ( 1 , 5 ) , ( 4 , 5 ) }

iii : { ( 1 , 3 ) , ( 4 , 3 ) }

iv : { ( 1 , 3 ) , ( 4 , 3 ) }

Explanation:

i ) : A x ( B U C )

= > { 1 , 4 } cross { elements of B and C, once }

= > { 1 , 4 } x { 2 , 3 , 5 }

= > { ( 1 , 2 ) , ( 1 , 3 ) , ( 1 , 5 ) , ( 4 , 2 ) , ( 4 , 3 ) , ( 4 , 5 ) }

ii ) : ( A x B ) U ( A x C )

= > ( { 1 , 4 } cross { 2 , 3 } ) U ( { 1 , 4 } cross { 3 , 5 } )

= > { ( 1 , 2 ) , ( 1 , 3 ) , ( 4 , 2 ) , ( 4 , 3 ) } U { ( 1 , 3 ) , ( 1 , 5 ) , ( 4 , 3 ) , ( 4 , 5 ) }

= > { ( 1 , 2 ) , ( 1 , 3 ) , ( 4 , 2 ) , ( 4 , 3 ) , ( 1 , 5 ) , ( 4 , 5 ) }

iii ) : A x ( common elements between B and C )

= > A x { 3 }

= > { ( 1 , 3 ) , ( 4 , 3 ) }

iv ) : Common elements between ( A x B ) and ( A x C )

= > common elements between { 1 , 4 } x { 2 , 3 } and { 1 , 4 } x { 3 , 5 }

= > common elements between { ( 1 , 2 ) , ( 1 , 3 ) , ( 4 , 2 ) , ( 4 , 3 ) } and { ( 1 , 3 ) , ( 1 , 5 ) , ( 4 , 3 ) , ( 4 , 5 ) }

= > { ( 1 , 3 ) , ( 4 , 3 ) }