If {1, k} ⊆ {1, 2, 3}, what is the set of possible values of k?
Answer and explanation
Correct answer: {1, 2, 3}
For {1, k} to be a subset of {1, 2, 3}, every element of the left-hand set must belong to the right-hand set. The element 1 already satisfies this condition, so k may be any of 1, 2, or 3. When k = 1, the set {1, k} is simply {1}, because repeated elements are not counted in a set; it is still a subset. Therefore the complete set of possible values is {1, 2, 3}, making option B correct.
Frequently asked questions
What is the correct answer to this question?
{1, 2, 3}
Why is this the correct answer?
For {1, k} to be a subset of {1, 2, 3}, every element of the left-hand set must belong to the right-hand set. The element 1 already satisfies this condition, so k may be any of 1, 2, or 3. When k = 1, the set {1, k} is simply {1}, because repeated elements are not counted in a set; it is still a subset. Therefore the complete set of possible values is {1, 2, 3}, making option B correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
