Could someone please explain these set theory functions to me?

Intersection means you take everything that is in BOTH sets, so A intersect B would be:

A intersect B = {II, V}

Union means you take everything that is in EITHER set. So A union B would be:

A union B = {I, II, III, IV, V, VI}

A relative complement (A complement B) means you take everything that is in A and remove everything that is in B

An absolute complement (A complement) means you take everything that is in the universe (U) and subtract everything that is in the set, it is equivalent to the relative complement (U complement A)

Example:

A complement = U complement A = {III, VI, VII, VIII}

So for 1.

B union C = everything in B or C = {II, III, IV, V, VI, VII}

now,

A insect (B union C) = everything in A and (B or C) = {II, IV, V}

2. Is similar to 1.

3.

(A complement B) = Everything in A that is not in B = {I, IV}

now

(A complement B) complement = U complement (A complement B) = Everything in U that is not in (A complement B) = {II, III, V, VI, VII, VIII}