question_answer

If A, B, C are three sets, then what is \[A-\left( ~B~-C \right)\]equal to?

A) \[A-(B\cap C)\]

B) \[(A-B)\cup C\]

C) \[(A-B)\cup (A\cap C)\]

D) \[(A-B)\cup (A-C)\]

Correct Answer: C

Solution :

[c] In the above Venn diagram, shaded area shows \[A-\left( BC \right).\] In the above Venn diagram, horizontal lines mean \[(A-B)\]and vertical lines mean \[(A\cap C)\] \[\therefore \]Total shaded portion, \[(A-B)\cup (A\cap C)=A-(B-C)\]