Consider the set A of all divisors of 30. How many subsets of A contains even divisors only?a)2b)16c)28d)4Correct answer is 'B'. Can you explain this answer?

Question

Answer

Set of divisors of 30={1,2,3,6,10,15,30} in these the even divisors r={2,6,10,30} we know no.of subsets to any set=2^n so answer is 2^4=16

Answer

The correct answer is not given because null set should not be included. so real subset of even divisors are 16-1 =15

Answer

A={2,3,5,6,10,15,30} P(A) even elements =2^4 becoz there are 4 even elements so answer is 16

Answer

Answer:

To find out how many subsets of A contain even divisors only, we need to first determine the divisors of 30 and then count the subsets that contain only even divisors.

Divisors of 30:
The divisors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.

Subsets of A containing even divisors:
To count the subsets of A that contain only even divisors, we need to consider the possible combinations of the even divisors of 30.

The even divisors of 30 are: 2, 6, 10, and 30.

Counting the subsets:
To count the subsets, we can use the concept of power set, which states that a set with n elements has 2^n subsets.

In this case, we have 4 even divisors, so the total number of subsets that can be formed using these even divisors is 2^4 = 16.

However, we need to exclude the empty set and the set containing all the even divisors, as these do not contain only even divisors.

Therefore, the number of subsets of A that contain even divisors only is 16 - 2 = 14.

Final Answer:
The correct answer is option B, 16.

Answer

Correct answer is 'B'. Even divisor of 30 = 2,6,10,30 No. of Even Divisors of 30 = 4 nP(A) = 2^n =2^4 = 16

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