.
Since the set R has 5 elements, the number of ALL its subsets is = 32.
See the lesson
- How many subsets are there in a given finite set of n elements?
in this site.
It includes the empty set and the subset coinciding with the given set.
The latest subset is called "improper".
All other subsets are called "proper".
So, the number of proper subsets is 32-1 = 31.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Miscellaneous word problems".