Question

4. By taking suitable sets A, B, C, verify the following results:

(i) A × (B ∩ C)=(A × B) ∩ (A × C).

Answer 1

Cartesian Product :
M x N is the set containing all the possible ordered pair (m ,n ) : m £ M and n £ N.
where £ means belongs to.

Steps :
1) Let A = { 1,2}
B ={ 3 }
C = { 4 }

Then,
LHS = A x ( B U C)
= { 1,2} x( { 3 } U {4} )
= { 1,2} x { 3,4 }
= (1,3 ) ,(1,4) , (2,3) , (2,4)

RHS = ( A x B) U ( A x C)
= ( { 1,2} x { 3} ) U ( {1,2} U {4} )
= (1,3) , (2,3) , ( 1,4) , (2,4)

Since, LHS = RHS

Answer 2

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