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The universal set \(U\) consists of all integers subsets of \(U\) are defined as...


Question

The universal set \(U\) consists of all integers subsets of \(U\) are defined as:
\(A = {y: y \leq 3}\)
\(B = {y: −5 < y < 12}\)
\(C = {y: −2 \leq y < 5}\)
\(A{\cap}(B{\cup}C)'\) is

Options

A) \(\{y < -4\}\)

B) \(\emptyset\)

C) \(\{y < 0\}\)

D) \(\{-4{\leq}y{\leq}3\}\)

The correct answer is A.

Explanation:

\(U = \{...,-3,-2,-1,0,1,2,...\}\)
\(A = \{...,-3,-2,-1,0,1,2\}\)
\(B = \{-4,-3,-2,-1,0,1,...,11\}\)
\(C= \{-2,-1,0,1,2,3,4\}\)
\((B{\cup}C)=\{...,-5,12,13,...\}\)
\(A{\cap}(B{\cup}C)=\{...,-5\}\)
\(=\{y<-4\}\)

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Dicussion (1)

  • \(U = \{...,-3,-2,-1,0,1,2,...\}\)
    \(A = \{...,-3,-2,-1,0,1,2\}\)
    \(B = \{-4,-3,-2,-1,0,1,...,11\}\)
    \(C= \{-2,-1,0,1,2,3,4\}\)
    \((B{\cup}C)=\{...,-5,12,13,...\}\)
    \(A{\cap}(B{\cup}C)=\{...,-5\}\)
    \(=\{y<-4\}\)

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