If A = {1, 4, 7, 10}, how many zero-element (empty) subsets are in P(A)?
Answer and explanation
Correct answer: 1
The power set P(A) is the set of all subsets of A. Every set, including a non-empty set such as A, has exactly one empty subset: the empty set ∅. Therefore P(A) contains exactly one zero-element subset. The number 4 is the number of elements in A, while 16 is the total number of subsets because |P(A)| = 2^4 = 16; neither represents the number of empty subsets.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The power set P(A) is the set of all subsets of A. Every set, including a non-empty set such as A, has exactly one empty subset: the empty set ∅. Therefore P(A) contains exactly one zero-element subset. The number 4 is the number of elements in A, while 16 is the total number of subsets because |P(A)| = 2^4 = 16; neither represents the number of empty subsets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
