Question

prove that c-(b-a) =(c intersection a) u(c intersection b')prove that C minus b minus A equal to C intersection b union c dash intersection b dash ​

Answer 1

SOLUTION

TO PROVE

$\sf{C - (B - A) =(C \cap A) \cup (C \cap B ') \: }$

PROOF

$\sf{C - (B - A) \: }$

$= \sf{C - (B \cap A ' ) \: }(by \: property \: of \: difference)$

$= \sf{C \cap (B \cap A ' )' \: }(by \: property \: of \: difference)$

$= \sf{C \cap \bigg(B ' \cup (A ' )' \bigg)\: }(by \: de \: morgan's \: law)$

$= \sf{C \cap (B ' \cup A )\: }$

$= \sf{(C \cap B ' )\cup (C \cap A )\: } \: (by \: distributive \: property)$

$= \sf{(C \cap A ) \cup (C \cap B ' ) \: } \: (by \:commutative \: property)$

Hence proved

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