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Power Set

If A=x:x ϵ W,...

Question

If $A = {x : x ϵ W, x < 2}, B = {x : x ϵ N, 1 < x < 5}$ and $C = {3, 5}$ then $A \times (B \cap C) =$

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Solution

Given : $A = {x : x ϵ W, x < 2}$ ,
$B = {x : x ϵ N, 1 < x < 5}$ and $C = {3, 5}$
$A = {0, 1}$
$B = {2, 3, 4}$
$C = {3, 5}$
$B \cap C = {2, 3, 4} \cap {3, 5}$
$\Rightarrow B \cap C = {3}$
$A \times (B \cap C) = {0, 1} \times {3}$
$∴ A \times (B \cap C) = {(0, 3), (1, 3)}$

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