Question

If A = {1,2,3........,10} then number of subsets of A containing only odd number is

• A. 31
• B. 32
• C. 27
• D. 30

Answer 1

Answer: (A)

31

Answer 2

Set A contains 5 odd numbers: {1, 3, 5, 7, 9}.
For each element, we have two choices: either include it in the subset or exclude it.
Since there are 5 odd numbers, we have $2^5 = 32$ possible subsets that contain only odd numbers.

However, we need to exclude the empty set since it does not contain any odd numbers. So the number of subsets of A containing only odd numbers is $32 - 1 = 31$. Therefore, the correct answer is option (A) 31.