If $A=\{f,l,o,w\}$ and $B=\{f,l,o,o,w\}$, then are A and B equal sets? If $A=\{f,l,o,w\}$ and $B=\{f,l,o,o,w\}$, are set $A$ and set $B$ equal?
I saw this example in my book. But what I had learnt is that two sets are said to be equal if they have same elements. 
Here, set $A$ and $B$ have same elements but their cardinal numbers are not same. In this case are $A$ and $B$ called equal?
 A: A set does NOT remember how many times it contains each element. It can answer only "yes" or "no" to the question "is such-and-such one of your elements?" -- and the totality of those yes/no answers is everything the set is.
Two sets $A$ and $B$ are the same if any which thing is either in both $A$ and $B$ or in neither of them.
In your case, $f$, $l$, $o$, and $w$ are all both in $A$ and $B$, and everything that is not one of those four things are in neither of $A$ and $B$.
A: We can say, by definition that $$A=B \Leftrightarrow A\subset B \text{ and } B \subset A$$ what is true in your case. 
It doesn't matter how many times you put the same element in the set. 
For example, if $A=\{a\}$ and $B=\{a,a\}$ we can see that if we take any element of $A$, which is $a$, this element we can find in $B$ and then $A\subset B$. 
Similarily, if we take any element of $B$, which is always $a$, we also can find it in $A$ and then $B\subset A$. 
So $A=B$.
A: Two sets, $X$ and $Y$, are equal if every element of $X$ is an element of $Y$ and each element of $Y$ is an element of $X$.
In your case, every element of $A$ is also an element of $B$, and every element of $B$ is also an element of $A$. Therefore, the two sets are equal.
A: Two sets are equal if they have same elements. If in any set any element is repeating. Still both are equal. 
They are not equal if any set containing element that other set doesn't have.
A: They are the same: each of $f$, $l$, $o$, and $w$ is in each of $A$ and $B$ but there are no other elements of $A$ and $B$. Repetitions are ignored.
