Question

- If set A = {x:x2 - 7x - 8 = 0), set B = {2,4}, set C = {4, 5, 6} then the value of A ~ (BNC) is equal to​

Answer 1

$\underline{\textbf{Given:}}$

$\mathsf{A=\{x\,|\;x^2-7x-8=0\}}$

$\mathsf{B=\{2,4\}}$

$\mathsf{C=\{4,5,6\}}$

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

$\mathsf{A{\cup}(B{\cap}C)}$

$\underline{\textbf{Solution:}}$

$\mathsf{Consider,}$

$\mathsf{A=\{x\;|\;x^2-7x-8=0\}}$

$\mathsf{A=\{x\;|\;(x-8)(x+1)=0\}}$

$\mathsf{A=\{-1,8\}}$

$\mathsf{B=\{2,4\}}$

$\mathsf{C=\{4,5,6\}}$

$\implies\mathsf{B{\cap}C=\{4\}}$

$\mathsf{Now,}$

$\mathsf{A{\cup}(B{\cap}C)}$

$\mathsf{=\{-1,8\}{\cup}\{4\}}$

$\mathsf{=\{-1,4,8\}}$

$\underline{\textbf{Find more:}}$

If U={x:x in N x<=30} A={x:x is prime <5} B={x:x is a perfect square <=10} and C={x:x is a perfect cube <=30} then verify the following results : (i) (A uu B)'=A'nn B' (ii)(A nn B)'=A'uu B' (iii) (A nn B)nn C=A nn(B nn C) (iv) A'-B'=B-A

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