Sets Relations And Functions Question 86
Question: Which one of the following is correct?
Options:
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 $
Show Answer
Answer:
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’ $
BETA
