Question

what is the number of subsets does vowels aeiou have

Answer 1

find subsets and make set of it:

P(A) = {φ,{a},{e},{i},{o},{u},{a,e},{a,i},{a,o},{a,u},{e,i},{e,o},{e,u},{i,o},{i,u},{o,u},{a,e,i},{a,e,o},{a,e,u},{a,i,o},{a,i,u},{a,o,u},{e,i,o},{e,i,u},{e,o,u},{i,o,u},{a,e,i,o},{a,e,i,u},{a,i,o,u},{e,i,o,u},{a,e,o,u},{a,e,i,o,u}}

elements in powerset are 2ⁿ=2⁵=32

combination of 1 element= ⁵C₁=5

combinations of 2 elemnts=⁵C₂=10

combinations of 3= ⁵C₃=10

combination of 4= ⁵C₄=5

combination of 5=⁵C₅=1

empty set φ=1

total subsets = 5+10+10+5+1+1=32

Thank you for asking the question,hope it helps!!!