集合A属于B,证明A和B的交集为A

集合A属于B,证明A和B的交集为A
那就是A包含于B吧。

for all x ∈ A∩B
=> x ∈ A and x ∈B
=> x ∈ A ( A is subset of B)
=> A∩B is subset of A --(1)
and
for all x ∈ A
=> x ∈ A and x ∈ B ( A is subset of B)
=> x ∈ A∩B
=> A is subset of A∩B ---(2)
from (1),(2),we have
A= A∩B

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