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P= {6, 7, 11, 12, 15)
Q = {4, 7, 12, 15, 20}
S = {3, 4, 11, 12, 16)
Given sets P, Q, and S above, which of the following sets represents S ∩ (P U Q) (the intersection of S with the union of sets P and Q)?o {3, 4, 7, 11, 12, 15, 16)
o {4, 6, 7, 11, 12, 15, 20}
O{4, 7, 12, 15)
O {4, 11, 12}

Respuesta :

We have to find the set that represents S ∩ (P ∪ Q).

We start by listing the elements that are in P or in Q to write the set P ∪ Q:

[tex]\begin{gathered} P=\lbrace6,7,11,12,14\rbrace \\ Q=\lbrace4,7,12,15,20\rbrace \\ P\cup Q=\lbrace4,6,7,11,12,14,15,20\rbrace \end{gathered}[/tex]

We now can intersect this last set with S, which will include only the elements that are both in P ∪ Q and S:

[tex]\begin{gathered} P\cup Q=\lbrace4,6,7,11,12,14,15,20\rbrace \\ S=\lbrace3,4,11,12,16\rbrace \\ S\cap(P\cup Q)=\lbrace4,11,12\rbrace \end{gathered}[/tex]

Answer: S ∩ (P ∪ Q) = {4,11,12} [Fourth option]

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