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vampirchik [111]
4 years ago
5

Let A, B and C be sets. Prove that if A ⊆ B ∪ C and A ∩ B = ∅ then A ⊆ C

Mathematics
1 answer:
Studentka2010 [4]4 years ago
6 0

Answer and Solution:

As per the question:

Given:

If A\subseteq B\cup C

A\cap B = \phi

To prove:

A\subseteq \C

Proof:

Suppose t\in A

As we know that:

A\subseteq B\cup C

Therefore,

t\in B or t\in C

Now, if we assume that t\in B

Then

t\in A\cap B

Since,

t\in A and t\in B

But

A and B are disjoint set and A\cap B = \phi

Therefore, this is contradictory.

Thus

t\notin B

So,

t\in C

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

Therefore, A\subseteq \C

Hence, proved.

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