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 $(A\cup B)'=B'$.