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
- A1
- B2
- C3
- D4
Solution & Step-by-step Explanation
First, let's write sets A and B in roster form by listing their unique distinct element letters:
A={B, E, L, O, W}
B={W, O, L}
Next, compute the relative set difference C=A−B, which includes elements present in A but completely absent from B:
C={B, E, L, O, W}−{W, O, L}
C={B, E}
The cardinality (number of elements) of set C is n(C)=2.
The total number of subsets for any given set containing n elements is given by the formula 2
n
:
Number of subsets of C=2
n(C)
=2
2
=4
A={B, E, L, O, W}
B={W, O, L}
Next, compute the relative set difference C=A−B, which includes elements present in A but completely absent from B:
C={B, E, L, O, W}−{W, O, L}
C={B, E}
The cardinality (number of elements) of set C is n(C)=2.
The total number of subsets for any given set containing n elements is given by the formula 2
n
:
Number of subsets of C=2
n(C)
=2
2
=4