If \(A=\{a,b,c,d\}\), how many two-element subsets of \(A\) are elements of the power set \(\mathcal{P}(A)\)?
Answer and explanation
Correct answer: 6
The power set \(\mathcal{P}(A)\) contains every subset of \(A\), including all its two-element subsets. To choose two elements from the four elements \(a,b,c,d\), use the combination formula \(\binom{4}{2}=\frac{4!}{2!2!}=6\). These subsets are \(\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}\). Therefore, option C, 6, is correct. The number \(2^4=16\) is the total number of subsets in \(\mathcal{P}(A)\), not the number of two-element subsets.
Frequently asked questions
What is the correct answer to this question?
6
Why is this the correct answer?
The power set \(\mathcal{P}(A)\) contains every subset of \(A\), including all its two-element subsets. To choose two elements from the four elements \(a,b,c,d\), use the combination formula \(\binom{4}{2}=\frac{4!}{2!2!}=6\). These subsets are \(\{a,b\},\{a,c\},\{a,d\},\{b,c\},\{b,d\},\{c,d\}\). Therefore, option C, 6, is correct. The number \(2^4=16\) is the total number of subsets in \(\mathcal{P}(A)\), not the number of two-element subsets.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
