Use the Venn diagram to find the number of elements in the...

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00:01 We are asked to use the venn diagram displayed here to compute these numbers here.

00:08 So the first one, a, is the number of elements in a union b.

00:14 So this can be also described as the number of elements in a or b.

00:20 Now a or b, a is indicated by this circle here, so it's represented by the circle, and b is represented by this circle.

00:30 So a or b includes this entire yellow shaded region.

00:37 All of the elements that fall within a or within b or within b.

00:42 So we add up all of these numbers and we get 31.

00:56 And then for b it's a number that are an a or b complement.

01:01 So this prime means the complement of the union of a or b.

01:07 So once again a or b union is this yellow shaded region.

01:15 So the complement of a union b is everything that is outside of the yellow shaded region.

01:22 So that is just the 7 and the 6.

01:26 So this one is 13.

01:32 And then for c we want the number that are in a intersect b.

01:36 This is the number that are in a and b.

01:40 So that is anything that's in both a and b.

01:44 So this is the overlap of the circles that represent events a and b.

01:49 So anything in this overlapped region of circles a and b...

Use the Venn diagram to find the number of elements in the given sets. (a) n(A?B) U A B 7 4 8 9 2 5 6 3 C (a) (b) (b) n(A?B') (c) n(B') (d) n(A?B') (e) n(A?B?C) (f) n(A') (g)