Answer to Question #162411 in Statistics and Probability for Nomhle Lukashe

Question

Let A and B be two sets defined in the universal set, U. Depict the following sets in Venn diagrams: (a) C = A ∩ B¯
∪ A¯ ∩ B
(b) D = (A ∩ B) ∪ (A ∩ B) (c) What can you say about the set C and 

Answer 1

Let $A$ and $B$ be two sets defined in the universal set $U$ .Then Venice diagrams of the given sets are given below

(a) $C=(A\cap \bar B) \cup (\bar A \cap B)$

$C=(A\cap \bar B) \cup (\bar A \cap B)$

(b) $D=(A\cap B)\cup (A\cap B)$ $=(A\cap B)$

$D= A\cap B$

(c) The set $C= (A\cup B)-(A\cap B)$