Discerete Mathematics Sets Empty Set Singleton Set How many

Discerete Mathematics

Sets

Empty Set

Singleton Set

How many elements are there in the following sets? Are the following sets all different?

Solution

for i) there is 1 element

for ii) there is 1 element

for iii) there is 1 element

for iv) there is 2 elements

and for v) there is 2 elements

No the following sets are not all different the last two are the same and the first 3 are the same. Although, given these sets all contain the null set which is basically just saying the sets do not have anything in them then you could say that all the sets are equivalent or have the same cardinal number(which means they have the same number of elements in the set)