Of the 3737 people at a basketball team party, 2525 of them play basketball, 1515 are under six feet tall, and 5 do not play basketball and are six feet or taller. Determine the number of people at the party who play basketball and are under six feet tall, |B∩?||B∩U|, where BB represents the set of people at the party who play basketball and? U represents the set of people at the party who are under six feet tall.

Question

Isabela Luna

Mathematics

3 March, 00:54

Of the 3737 people at a basketball team party, 2525 of them play basketball, 1515 are under six feet tall, and 5 do not play basketball and are six feet or taller. Determine the number of people at the party who play basketball and are under six feet tall, |B∩?||B∩U|, where BB represents the set of people at the party who play basketball and? U represents the set of people at the party who are under six feet tall.

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Atlas · Answer 1

8

Step-by-step explanation:

Universal Set, U=37

Number who play basketball, n (B) = 25

Number who are under six feet, n (U) = 15

Number of those who do not play basketball and are six feet or taller, n (B∪U) '=5

From set theory.

U=n (B) + n (U) - n (B∩U) + n (B∪U) '

37=25+15-n (B∩U) + 5

37=45-n (B∩U)

Therefore:

n (B∩U) = 45-37=8

Therefore, the number of people at the party who play basketball and are under six feet tall is 8.