Question

1) If n (AXB) n (AXC) = 8 and n(BnC)=2 then n(A) is​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{n[(A{\times}B){\cap}(A{\times}C)]=8\;\;\&\;\;n(B{\cap}C)=2}$

$\underline{\textsf{To find:}}$

$\mathsf{n(A)}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{n[(A{\times}B){\cap}(A{\times}C)]=8}$

$\mathsf{n[A{\times}(B{\cap}C)]=8}$

$\textsf{But}\;\;\boxed{\mathsf{n(A{\times}B)=n(A){\times}n(B)}}$

$\implies\mathsf{n(A)\,{\times}\,n(B{\cap}C)=8}$

$\implies\mathsf{n(A){\times}2=8}$

$\implies\mathsf{n(A)=\dfrac{8}{2}}$

$\implies\boxed{\mathsf{n(A)=4}}$

$\underline{\textsf{Answer:}}$

$\textsf{n(A)=4}$

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