1. D: The overlap of the two sets represents the intersection, which is the set of elements common to both sets M and C. In this case, it's the set {4, 5, 6}.
2. D: P is the set of the first 100 multiples of 8 (8*1 = 8, 8*2 = 16, and so on)
3. C: n(A) represents the number of elements in the set A. When
[tex]n(A\cup B)=n(A)+n(B)[/tex]
that means the sets A and B are disjoint, represented by the two circles with no overlap.
4. E:
[tex]A\cup B[/tex] is the set of elements belonging to either set A or B. The three elements of A are all in B, so A is a subset of B. This means [tex]A\cup B=B[/tex].
Because A is a subset of B, we have [tex]A\cap B=A[/tex].
[tex](A\cup B)'[/tex] is the complement of [tex]A\cup B[/tex], which refers to the set of elements *not* belong to [tex]A\cup B[/tex]. These are all the numbers in U that are not in this union, which would be [tex](A\cup B)'=\{3,13\}[/tex].
Because we know [tex]A\cup B=B[/tex], we have [tex](A\cup B)'=B'[/tex].
