If A has 6 elements, how many elements does the power set P(A) have in total?
Answer and explanation
Correct answer: 64
For a finite set with n elements, the number of members of its power set is 2ⁿ. Each of the six elements of A can either be selected or not selected when forming a subset, producing 2 × 2 × 2 × 2 × 2 × 2 = 2⁶ possibilities. Since 2⁶ = 64, the power set P(A) contains 64 subsets. Therefore option D is correct; 32 is only 2⁵.
Frequently asked questions
What is the correct answer to this question?
64
Why is this the correct answer?
For a finite set with n elements, the number of members of its power set is 2ⁿ. Each of the six elements of A can either be selected or not selected when forming a subset, producing 2 × 2 × 2 × 2 × 2 × 2 = 2⁶ possibilities. Since 2⁶ = 64, the power set P(A) contains 64 subsets. Therefore option D is correct; 32 is only 2⁵.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
