If A = {x : x is a letter in word BELOW}, B = {x : x is a letter in word WOOL}…
20172021
If A = {x : x is a letter in word BELOW}, B = {x : x is a letter in word WOOL} and C = A - B, then the number of subsets of C is:
- A.
1
- B.
2
- C.
3
- D.
4
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Correct answer: D
Concept: For a set X with n distinct elements, the total number of subsets of X (its power set) equals 2n, since each element is either included or excluded. Also, the set difference A - B consists of exactly those elements of A that do not belong to B.
Set A collects the distinct letters of BELOW: A = {B, E, L, O, W} (5 distinct letters).
Set B collects the distinct letters of WOOL: B = {W, O, L} (the repeated O is counted only once, so B has 3 distinct letters).
C = A - B removes from A every letter that also occurs in B: removing W, O and L from A leaves C = {B, E}.
C has 2 distinct elements, so the number of subsets of C is 22 = 4.
Listing every subset of {B, E} directly confirms this: the empty set {}, the singletons {B} and {E}, and the full set {B, E} — exactly 4 subsets in total, matching 22 = 4.