Arrange the following sets in increasing order, on the basis of their cardinality :
A. A1 = {{1, 2}, {3}},
B. A2 = {{1}, {2}, {3}, {4}}
C. A3 = {{1, 2, 3, 4, 5, 6}}
D. A4 = {{1, 2}, {2, 3, 4}, {5}}
E. A5 = {{1}, {2}, {3}, {4}, {5}}
Choose the correct answer from the options given below :
Solution
The correct answer is C, A, D, B, E
Explanation:
To determine the correct answer, we can find the cardinality (i.e., the number of elements) of each set.
- A1 = {{1, 2}, {3}} has 2 elements.
- A2 = {{1}, {2}, {3}, {4}} has 4 elements.
- A3 = {{1, 2, 3, 4, 5, 6}} has 1 element.
- A4 = {{1, 2}, {2, 3, 4}, {5}} has 3 elements.
- A5 = {{1}, {2}, {3}, {4}, {5}} has 5 elements.
Now, we arrange them in increasing order of their cardinalities:
- A3 = {{1, 2, 3, 4, 5, 6}} has 1 element.
- A1 = {{1, 2}, {3}} has 2 elements.
- A4 = {{1, 2}, {2, 3, 4}, {5}} has 3 elements.
- A2 = {{1}, {2}, {3}, {4}} has 4 elements.
- A5 = {{1}, {2}, {3}, {4}, {5}} has 5 elements.
The correct order is A3, A1, A4, A2, A5.
So, the correct answer is: C, A, D, B, E