why does he add one

Look at the *Note* below the question, it says “every set is a subset of itself”. Meaning set {4,19,1,6} is a subset of {4,19,1,6}. Let me put it this way

no. of sets with 1 element like {4}, {19},… = 4

no of sets with 2 elements like {4, 19}, {19, 6}… = 6

no of sets with 3 elements like {4, 19, 1}… = 4

no of sets with 4 elements {4,19,1,6} = 1. Total = 15

i thought the same but a really got hung up on the phrase every set is a subset of it self i thought that no. of set with 2 elements can be {4,19} and {19,4} so it would be 12 and so on.

what made you determine it wouldn’t be that case that i mentioned above

A set is nothing but a collection of numbers. So, {4,19} and {19,4} are essentially the same sets as the order of the numbers doesn’t matter. I hope, this helped you.

ok so the rule of thumb should be a set cannot have repeats and the order of numbers in any set dose not matter is that right

Not exactly, a set can have repeated elements eg: {1,2,2,2,3}, but it is no different from {2,1,2,3,2}. They are both same, and it is in the context the order doesn’t matter. If you have to calculate mean, median and mode for the values in the set, you **must** arrange them in ascending order.

a set cannot have repeated elements i am pretty sure i have heard the same on GRE Quant concept series

Sorry It’s my bad. You are correct, I cross checked it and a set by definition can’t have repeated elements. One with repeated elements is called a multiset. Yes, a set is a collection of elements where repetition and order are ignored.