Solution to Use algebra of sets to prove that, [(𝐵 − 𝐴)' ∩ 𝐴] − 𝐴' = … - Sikademy
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Archangel Macsika

Use algebra of sets to prove that, [(𝐵 − 𝐴)' ∩ 𝐴] − 𝐴' = 𝐴

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Solution:

LHS=[(𝐵 − 𝐴)' ∩ 𝐴] − 𝐴' \\=[(𝐵' − 𝐴')∩ 𝐴] − 𝐴'

=[(𝐵' − 𝐴') ∩ 𝐴] ∩ [𝐴']' \ \ [\because P-Q=P∩Q']

=[(𝐵' − 𝐴') ∩ 𝐴] ∩ A \\=(𝐵' − 𝐴') ∩ 𝐴∩ 𝐴 \\=(𝐵' − 𝐴') ∩ 𝐴

\\=(𝐵 − 𝐴)' ∩ 𝐴 \\=A-(B-A) \\=A \\=RHS

Hence, proved.

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Question ID: mtid-5-stid-8-sqid-1350-qpid-1088