Set — Important Questions

∅, {1, 2}, {1, 2, 3, 4}

A subset contains only elements that are also in the original set. ∅ is a subset of every set. {1, 2} ⊆ A since 1, 2 ∈ A. {1, 2, 3, 4} = A, so A ⊆ A. {5} and {1, 5} contain element 5 which is not in A.

5

A = {x : x is a natural number less than 6} means A = {1, 2, 3, 4, 5}. Natural numbers start from 1. Numbers less than 6 are 1, 2, 3, 4, 5. Therefore n(A) = 5.

{1, 3, 5}

A - B contains elements that are in A but not in B. Since A = {1, 3, 5} and B = {2, 4, 6}, no element of A is in B. Therefore A - B = {1, 3, 5} = A.

17

Using the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B). Substituting values: n(A ∪ B) = 12 + 8 - 3 = 17. We subtract n(A ∩ B) to avoid counting common elements twice.