If A and B be two sets such that

Question:

If $A$ and $B$ be two sets such that $n(A)=3, n(B)=4$ and $n(A \cap B)=2$ then find.

(i) $n(A \times B)$

(ii) $n(B \times A)$

(iii) $n(A \times B) \cap(B \times A)$

 

Solution:

Given: $n(A)=3, n(B)=4$ and $n(A \cap B)=2$

(i) $n(A \times B)=n(A) \times n(B)$

$\Rightarrow n(A \times B)=3 \times 4$

$\Rightarrow n(A \times B)=12$

(ii) $n(B \times A)=n(B) \times n(A)$

$\Rightarrow n(B \times A)=4 \times 3$

$\Rightarrow \mathrm{n}(\mathrm{B} \times \mathrm{A})=12$

(iii) $n((A \times B) \cap(B \times A))=n(A \times B)+n(B \times A)-n((A \times B) \cup(B \times A))$

$n((A \times B) \cap(B \times A))=n(A \times B)+n(B \times A)-n(A \times B)+n(B \times A)$

$n((A \times B) \cap(B \times A))=0$

 

 

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