- #1
22990atinesh
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Homework Statement
Prove that ##A\cap(B\Delta C)=(A\cap B)\Delta(A\cap C)##
Homework Equations
The Attempt at a Solution
[/B]
L.H.S.=##A\cap(B\Delta C)##
=##A\cap[(B - C) \cup (C - B)]##
=##A\cap[(B \cap \bar{C}) \cup (C \cap \bar{B})]##
=##[A\cap (B \cap \bar{C})] \cup [A\cap (C \cap \bar{B})]##
=##[(A\cap B) \cap \bar{C}] \cup [(A\cap C) \cap \bar{B}]##
R.H.S.=##(A \cap B) \Delta (A \cap C)##
=##[(A \cap B) - (A \cap C)] \cup [(A \cap C) - (A \cap B)]##
=##[(A\cap B) \cap \bar{(A\cap C)} ] \cup [(A\cap C) \cap \bar{(A\cap B)}]##
=##[(A\cap B) \cap (\bar{A} \cup \bar{C})] \cup [(A\cap C) \cap (\bar{A} \cup \bar{B})]##
I tried to make L.H.S = R.H.S. But with above results, It's not possible. Can anyone tell me what I've assumed wrong.