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

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

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

4. E:

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 .

Because A is a subset of B, we have .

is the complement of , which refers to the set of elements *not* belong to . These are all the numbers in U that are not in this union, which would be .

Because we know , we have .

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions