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jolli1 [7]
3 years ago
12

Use Use an element argument to prove the state (A-B)U(ANB) = A" is true. he statement "For all sets A and B,

Mathematics
2 answers:
lys-0071 [83]3 years ago
3 0

Answer with Step-by-step explanation:

We have to prove that

(A-B)\cup (A\cap B)=A is true for all sets A and B

Let x\in(A-B)\cup (A\cap B)

Then x\in(A-B) or x\in(A\cap B)

x\in A and x\notin B or x\in A\;and\; x\in B

Hence, x\in A

Conversely ,Let x\in A

Then x belongs to A and x does not belongs to B then

x belongs to A- B

Or  x belongs to A and x belongs to B then x belongs to A \cap B

Hence, x\in( A-B)\cup (A\cap B)

Therefore, (A-B)\cup (A\cap B)=A

ozzi3 years ago
3 0

Answer with explanation:

To Prove: (A -B) ∪ (A ∩ B)=A

Proof:

Consider two sets A and B

⇒⇒ To prove A=B, in sets

We need to prove

A ⊆ B

and , B ⊆ A

then , A=B.

→A - B ⊆ A and A ∩ B ⊆ A

So, there are two possibilities

Either,→A⊆ A-B ∪ (A ∩ B) --------(1)

Or,→ A -B ∪ (A ∩ B)⊆ A-----------(2)

Combining (1) and (2) , we get

(A -B) ∪ (A ∩ B)=A

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