A) \[A\cup (B-C)=A\cap (B\cap C')\]
B) \[A-(B\cup C)=(A\cap B')\cap C'\]
C) \[A-(B\cap C)=(A\cap B')\cap C\]
D) \[A\cap (B-C)=(A\cap B)\cap C\]
Correct Answer: B
Solution :
[b]Let a Venn-diagram be drawn taking three intersecting sets A, B and C under a universal set U. This makes 8 regions a to h as shown.A has region a, b, d, e |
B has region b, c, e, f |
C has regions d, e, f, g |
C? has regions a, b, c, h |
B? has regions a, b, g, h |
Statement : \[A\cup (B-C)=A\cap (B\cap C)\] |
\[LHS\equiv (a,b,e,d)\cup b,c\equiv a,b,c,d,e.\] |
\[RHS\equiv a,b,d,e\cap e,f\equiv e,\] |
So, statement [a]is not correct. |
Statement : \[A-(B\cup C)=(A\cap B')\cap C'\] |
\[LHS\equiv (a,b,d,e)-(b,c,d,e,f,g)\equiv a.\] |
\[RHS\equiv (a,b,d,e\cap a,d,g,h)\cap (a,b,c,h)\equiv a,\] |
So, statement [b]is correct. |
Correct statement is: |
\[A-(B\cup C)=(A\cap B')\cap C'\] |
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