Let A = {X : X ⊆ {1, 2, 3, 4}, {1, 4} ⊆ X, and 2 ∉ X}. Which set is equal to A?
Answer and explanation
Correct answer: {{1, 4}, {1, 3, 4}}
Each member X of A must contain both 1 and 4 because {1,4} ⊆ X. The element 2 is forbidden, so it cannot occur in X. The only remaining element from the universal set is 3, and it can be either omitted or included. Consequently, the only possibilities are X = {1,4} and X = {1,3,4}. Thus A = {{1,4}, {1,3,4}}, making option A correct. The other choices either include the forbidden element 2 or omit a required element.
Frequently asked questions
What is the correct answer to this question?
{{1, 4}, {1, 3, 4}}
Why is this the correct answer?
Each member X of A must contain both 1 and 4 because {1,4} ⊆ X. The element 2 is forbidden, so it cannot occur in X. The only remaining element from the universal set is 3, and it can be either omitted or included. Consequently, the only possibilities are X = {1,4} and X = {1,3,4}. Thus A = {{1,4}, {1,3,4}}, making option A correct. The other choices either include the forbidden element 2 or omit a required element.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
