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Step-by-step explanation:
A = { 1,2,3,4 }
B = { 3,4,5,6 }
C = { 2,4,6 }
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B U C = { 2,3,4,5,6 }
A ∩ B = { 3,4 }
A ∩ C = { 2,4 }
A ∩ ( B U C ) = { 2,3,4 }
( A ∩ B ) U ( A ∩ C ) = { 2,3,4 }
-------------------------------------------------------
{ 2,3,4 } = { 2,3,4 }
:. A ∩ ( B U C ) = ( A ∩ B ) U ( A ∩ C )
hence proved.
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