2. Out of the 385 athletes, 54 play volleyball, 67 play...

2. Out of the 385 athletes, 54 play volleyball, 67 play soccer and 27 play both. Using a Venn diagram and answer the following questions a) Venn diagram. [2] b) How many athletes play volleyball and not soccer? [2] c) How many athletes play volleyball or soccer? [2] d) How many play neither volleyball nor soccer? [1]

Transcript

00:01 In this question, we're given that there are 385 athletes.

00:04 54 play volleyball, 67 play soccer, 27 play both.

00:10 I'm going to let the set u be the universal set, v with a volleyball set and sbd soccer sets.

00:17 So that means the number of players in the universal set will be 385.

00:27 And the number of players in the volleyball set, there is number of elements in the set v will be 54, volleyball.

00:38 And number of players in the soccer set will be number of elements in the set s will be 67.

00:46 And we also have number of players in both sets.

00:50 Now in both sets, sets in end means intersect or means union.

01:02 In both sets means set v and s.

01:06 So vn will be intersects.

01:13 Playing both will be 27.

01:16 So there are 27 players in both sets at the same time.

01:21 Now let's draw the venn diagram.

01:25 This is your universal set, and you have your sets v and your set s.

01:31 Now there are 27 in both sets, so i'm going to put 27 over here.

01:36 And now over here would be the entire set v that will be 54 of them minus 27 so to get just this part here so over here will be 54 minus 27 and that will be equals to 27 now over here as only would be taking from the entire set of s that is 67 of them minus of 27 and so that will be 40.

02:15 So out over here, what is outside of these two set will be 385 minus 27 plus 27 plus 40...

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