Let a, b and c be sets. prove that if a ⊆ b ∪ c and a ∩ b = ∅ then a ⊆ c

Answer and Solution:

As per the question:

Given:

If

To prove:

Proof:

Suppose

As we know that:

Therefore,

or

Now, if we assume that

Then

Since,

and

But

A and B are disjoint set and

Therefore, this is contradictory.

Thus

So,

Every element in the set A is also present in the set C

Therefore,

Hence, proved.