Show that A ∩ B = A ∩ C need not imply B = C.

Open in App

Solution

Let’s assume,

A={ 1,2 } B={ 1,3 } C={ 1,4 }

A∩B={ 1,2 }∩{ 1,3 } ={ 1 } (1)

A∩C={ 1,2 }∩{ 1,4 } ={ 1 } (2)

From equation (1) and (2),

A∩B=A∩C

Hence,

A∩B=A∩C

But,

B ≠ C

Because 3∈B , 3∉C

Thus, it is proved that A∩B = A∩C need not imply B = C.

Suggest Corrections

Similar questions

Show that A intersection B is equal to A intersection C need not imply B=C

\to a \times \to b = \to a \times \to c

\to b = \to c

For three sets A, B and C, show that

(i) $A \cap B = A \cap C$ need not imply B = C.

(ii) $A \subset B \Rightarrow C - B \subset C - A$

\div

\times

Join BYJU'S Learning Program