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The players on a soccer team wear shirts, with each player having one of the numbers $1, 2, ..., 11$ on their backs. The set $A$ contains players with even numbers on their shirts. The set $B$ comprises players wearing an odd number less than $7$. The set $C$ contains the defenders, which are those wearing numbers less than $6$. Select the correct set that corresponds to each of the following.

$A∩(B∪C)$

$B. \{2\}$

$D. \{2,4\}$

$E. \{1,3,5\}$

I have eliminated $2$ answers and these are the remaining ones. I am thinking it's $E$ since those numbers applies to both $B$ and $C$.

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    Maybe the simplest thing to do is to notice that $A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$. – 2017-01-31

2 Answers 2

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$A = \{2,4,6,8,10\}$

$B = \{1,3,5\}$

$C = \{1,2,3,4,5\} \supset B$

Therefore $A \cap ( B \cup C ) = A \cap C = \{ 2 , 4 \}$.

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I have eliminated 2 answers and these are the remaining ones. I am thinking it's E since those numbers applies to both B and C.

No, that is a union symbol between those literals, which means one of $B$ or $C$.

In full: "$A$ and ( $B$ or $C$ )".

$A\cap (B\cup C)$ thus comprises "players with even numbers on their shirts ($A$), who either: wear an odd number less than 7 ($B$) or wear numbers less than 6 ($C$)."   That clearly leaves us with players wearing even numbers less than 6, which are $\{2,4\}$