Use an element argument to prove each statement. assume that all sets are subsets of a universal set u.
for all sets a, b, andc, if a ⊆ b then a∪c ⊆ b∪c

We are asked to prove the statement,

For all sets A, B, and C, if A ⊆ B then A∪C ⊆ B∪C

Let us consider set A as:

         A={1,3,4,5}

and B={1,2,3,4,5,6,7}

Clearly we may observe that A is a subset of B.

( Since, all the elements of set A are contained in set B .

Hence, A is a subset of B)

Now let us consider set C as:

C={1,2}

Hence,

A∪C={1,2,3,4,5}

and

B∪C={1,2,3,4,5,6,7}

Still we observe that:

          A∪C ⊆ B∪C

Since all the elements of the set A∪C are contained in the set B∪C.

b

step-by-step explanation: