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How To Proof Set A Is Equal To Set B

Some people are wrong ways to prove that set A is equal to set B. I also experienced it when I started learning math. Though the concept of set A is equal to set B very simple. We only have to prove that set A is a subset of set B and set B is a subset of set A. Of course the basic is very easy to understand.

Then, how to prove the set A is a subset of the set B, vice versa?

The way to prove set A is a subset of set B is by taking any element on set A and then prove that element is a element of set B. It can be easily understood that the taking of any element can be representative of all element of the set. Mathematically like this :

    \[A=B\Longleftrightarrow\left(A\subseteq B\right)\wedge\left(B\subseteq A\right)\]

with

    \[A\subseteq B\Longleftrightarrow\left(\left(x\in A\right)\Rightarrow\left(x\in B\right)\right)\]

Example : (more…)