Use Use an element argument to prove the state (A-B)U(ANB) = A" is true. he statement "For all sets A and B,
2 answers:
Answer with Step-by-step explanation:
We have to prove that
is true for all sets A and B
Let 
Then
or 
and
or 
Hence,
Conversely ,Let 
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 
Hence, 
Therefore, 
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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