### Theory:

If two finite sets $$A$$ and $$B$$ have the same number of elements, then they are called equivalent sets. It is denoted by $A\approx B$. If $$A$$ and $$B$$ are equivalent sets, then $$n(A) = n(B)$$.
Example:
1.  Consider the set $A\phantom{\rule{0.147em}{0ex}}=\phantom{\rule{0.147em}{0ex}}\left\{c,d\right\}$ and $B=\phantom{\rule{0.147em}{0ex}}\left\{1,2\right\}$.

Here the sets $$A$$ and $$B$$ are equivalent sets as $$n(A) = n(B) = 2$$.

2.  Consider the set $A=\phantom{\rule{0.147em}{0ex}}\left\{x:x\phantom{\rule{0.147em}{0ex}}\in \mathrm{ℕ},2 and the set of all months in a year having $$31$$ days.
Here the set $$A$$ belongs to natural number between $$2$$ and $$10$$.

That is, $A=\phantom{\rule{0.147em}{0ex}}\left\{3,4,5,6,7,8,9\right\}$

And let the set of all months in a year having $$31$$ days be $$B$$.

The months having 31 days in a year are January, March, May, July, August, October and December. That is, $B=\phantom{\rule{0.147em}{0ex}}\left\{\mathit{January},\phantom{\rule{0.147em}{0ex}}\mathit{March},\phantom{\rule{0.147em}{0ex}}\mathit{May},\phantom{\rule{0.147em}{0ex}}\mathit{July},\phantom{\rule{0.147em}{0ex}}\mathit{August},\phantom{\rule{0.147em}{0ex}}\mathit{October},\phantom{\rule{0.147em}{0ex}}\mathit{December}\right\}$.

The sets $$A$$ and $$B$$ has $$6$$ elements in it. Thus, $$n(A) = n(B) = 6$$.
If two sets $$A$$ and $$B$$ are equal sets, then they contain exactly the same elements; otherwise, they are said to be unequal.
Important!
• For equal sets, each element of set $$A$$ belongs to set $$B$$ and vice versa.
• All equal sets are equivalent sets, but all equivalent sets are need not be equal sets.
Example:
Consider the set $A=\phantom{\rule{0.147em}{0ex}}\left\{\mathit{Red},\mathit{Orange},\mathit{Yellow},\mathit{Green},\mathit{Blue},\mathit{Indigo},\mathit{Violet}\right\}$. Another set contains the set of all colour codes in the rainbow.

Here the set $$A$$ is given in roaster form. Let us express the set $$B$$ also in roaster form.

The colour codes of rainbow follow VIBGYOR.  That is Violet, Indigo, Blue, Green, Yellow, Orange and Red.

Thus, $B=\phantom{\rule{0.147em}{0ex}}\left\{\mathit{Violet},\mathit{Indigo},\mathit{Blue},\mathit{Green},\mathit{Yellow},\mathit{Orange},\mathit{Red}\right\}$.

Therefore, both sets $$A$$ and $$B$$ have the same elements. So they are equal sets.
Important!
• If the sets $$A$$ and $$B$$ are equal, then $$A=B$$.
• If the sets $$A$$ and $$B$$ are unequal, then $$A≠B$$.