If A, B and C are three sets such that A B = A C and A B = A C th… - Vidyadip

MCQ

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
$A = C$
✓
$B = C$
C
$\;A \cap B = \emptyset $
D
$\;A = B$

✓

Answer

Correct option: B.

$B = C$

b
$A \cup B=A \cup C$

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

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

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

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