The number of subsets of a set with n elements is 2^n. Here, n = 3, so 2^3 = 8.

The power set of a set with n elements has 2^n subsets. Here, n=3, so the power set has 2^3 = 8 subsets.

The Cartesian product A × B consists of all ordered pairs (a, b) where a ∈ A and b ∈ B. Thus, A × B = {(1, x), (2, x)} for all odd integers x.

The intersection A ∩ B includes all prime numbers less than 10, which are {2, 3, 5, 7}.

The natural numbers less than 5 are {1, 2, 3, 4} and the prime numbers are {2, 3}. Their intersection is {2, 3}.

A is the set of all even integers, while B is the set of multiples of 4. Not all even integers are multiples of 4 (e.g., 2 is even but not a multiple of 4), hence A is not a subset of B.

The power set of a set with n elements has 2^n subsets. Here, n = 4, so the power set has 2^4 = 16 subsets.

The number of subsets of a set with n elements is 2^n. Here, n=2, so the number of subsets is 2^2 = 4.

The power set of B = {a, b} is {∅, {a}, {b}, {a, b}}.

The total number of subsets is 2^4 = 16. Proper subsets exclude the set itself, so there are 16 - 1 = 15 proper subsets.

The proper subsets of a set exclude the set itself. For C = {1, 2}, the proper subsets are {∅}, {1}, and {2}, totaling 3 subsets.

The set C = {2, 3, 5, 7}. The power set of C includes all subsets, including the empty set, so it is {{}, {2}, {3}, {5}, {7}, {2, 3}, {2, 5}, {2, 7}, {3, 5}, {3, 7}, {5, 7}, {2, 3, 5}, {2, 3, 7}, {2, 5, 7}, {3, 5, 7}, {2, 3, 5, 7}}.

The even integers less than 10 are 0, 2, 4, 6, and 8.

The power set of an infinite set is also infinite. Since C contains all even integers, its power set is infinite.

The set {2, 4, 6} contains only even integers, making it a subset of C.

The number of ways to choose 3 elements from a set of 6 is given by the combination formula C(n, r) = n! / (r!(n-r)!). Here, C(6, 3) = 20.

The total number of subsets of D is 2^4 = 16. Proper subsets are all subsets except the set itself, so there are 16 - 1 = 15 proper subsets.

The total number of subsets is 2^4 = 16. Proper subsets exclude the set itself, so 16 - 1 = 15.

A subset must contain elements from the original set. {4} is not a subset of D.

The proper subsets of D = {1, 2} are {∅}, {1}, and {2}. So, there are 3 subsets, but excluding D itself gives us 2 proper subsets.

The power set of D = {1, 2} is {∅, {1}, {2}, {1, 2}} which contains 4 subsets.

A subset can only contain elements from the original set. {3} is not a subset of D.

A subset can only contain elements from the original set. {1} is not a subset of D.

The number of subsets of a set with n elements is 2^n. Here, n = 2, so 2^2 = 4.

The subsets containing 'a' are {a}, {a, b}, so there are 2 subsets.

If 1 is included, we can choose from the remaining 4 elements (2, 3, 4, 5). The number of subsets is 2^4 = 16.

The total number of subsets is 2^4 = 16. Proper subsets exclude the set itself, so there are 16 - 1 = 15 proper subsets.

The power set of a set with n elements has 2^n elements. Here, n = 2, so 2^2 = 4.

The subsets containing 1 are {1}, {1, 2}, and the empty set is not included.

The total number of subsets is 2^4 = 16. Proper subsets exclude the set itself, so 16 - 1 = 15.