Question

If your good with set theory, i need help with the first four questions!

Answer 1

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

`n(A\cup B)=n(A)+n(B)`

that means the sets A and B are disjoint, represented by the two circles with no overlap.

4. E:

`A\cup B` 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
`A\cup B=B`.

Because A is a subset of B, we have
`A\cap B=A`.

`(A\cup B)'` is the complement of
`A\cup B`, which refers to the set of elements *not* belong to
`A\cup B`. These are all the numbers in U that are not in this union, which would be
`(A\cup B)'=\{3,13\}`.

Because we know
`A\cup B=B`, we have
`(A\cup B)'=B'`.