Verify that (AUB)’=A’n B’

Assuming denotes the complement of the set , i.e. all elements in the universal set that do not belong to , then we can prove this in general.

To establish equality between two sets, you need to show that they are both subsets of one another.

Let .

By definition of set complement, this means .

By definition of set union, and .

By definition of complement, and .

By definition of set intersection, .

Therefore is a subset of , because membership of some arbitrary element in the first set directly implies membership in the second set.

Let . The proof follows similarly as above.

By definition of intersection, and .

By definition of complement, and .

By definition of union, .

By definition of complement, .

Therefore is a subset of .

And hence both sets are equal, regardless of what the sets may be.

a thesis statement is not a fact or a question

step-by-step explanation:

a thesis statement is a topic it is not a fact or a question