If A = {a, b, c, d, e}, how many elements of P(A) contain a but do not contain both b and c?
Answer and explanation
Correct answer: 12
We count subsets of A that must contain a and must not contain both b and c. The element a is fixed as included. For b and c, the allowed choices are neither, b only, or c only, giving 3 choices; the choice containing both is excluded. Elements d and e are independent, with 2 choices each. Therefore the total is 1 × 3 × 2 × 2 = 12.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
We count subsets of A that must contain a and must not contain both b and c. The element a is fixed as included. For b and c, the allowed choices are neither, b only, or c only, giving 3 choices; the choice containing both is excluded. Elements d and e are independent, with 2 choices each. Therefore the total is 1 × 3 × 2 × 2 = 12.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
