If A, B and C are three sets such that A cap B = A cap C and A cup B = A cup C then

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1.Set Theory

easy

If $A, B$ and $C$ are three sets such that $A \cap B = A \cap C$ and $A \cup B = A \cup C$ then

A

$A = C$

B

$B = C$

C

$\;A \cap B = \emptyset $

D

$\;A = B$

(AIEEE-2009)

Solution

$A \cup B=A \cup C$

$\Rightarrow n(A \cup B)=n(A \cup C)$

$\Rightarrow n(A)+n(B)-n(A \cap B)$

$=n(A)+n(C)-n(A \cap C)$

Standard 11

Mathematics

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