If ACB then
AUB =
AnB =
A-B =
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Step-by-step explanation:
First, assume that A ⊆B and we have to prove that A ∩B = A
Proof: Given A ⊆B
Let x ∈ A ∩ B which implies that x ∈ A and x ∈B. Hence we can imply that
A ∩ B ⊆ A (We started with an element in A ∩ B and concluded that it is in A)
——(1)
Now, let x ∈ A which implies x ∈B (as A ⊆B)
Hence, x ∈ A ∩ B, which in turn implies
A ⊆ A ∩ B ——-(2)
From (1) and (2), A ∩B = A
Conversely, assume A ∩B = A and we have to prove that A ⊆B
Proof: Given A ∩B = A
Let x ∈ A , then since A ∩B = A , x ∈ A ∩ B
This implies x ∈B, hence in turn implies A ⊆B (We have an element in A and we proved that it is in B).
Hence proved.
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