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Show that {A}{B}={A}{B}implies {A}={B}

Question

Show that $A \cap B = A \cap B$ implies $A = B$

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Show that

A \cap B = A \cap B

implies

A = B

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11 mins ago

Text solutionVerified

Solution: let a be an element

a \in A

then

a \in (A \cup B)

\Rightarrow a \in (A \cap B)

(given)
so,

a \in B

b \in B

then

b \in (A \cup B)

\Rightarrow b \in (A \cap B) \Rightarrow b \in A

that means for all \displaystyle{a}\in{A},{a}\in{B}&{b}\in{B},{b}\in{A}
so,

A = B

hence proved

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Question Text	Show that $A \cap B = A \cap B$ implies $A = B$
Answer Type	Text solution:1
Upvotes	150