If A = {2, 3, 5, 7, 11} and B = {x ∈ A | x + 1 ∈ A}, what is A \ B?
Advertisement
Answer and explanation
Correct answer: {3, 5, 7, 11}
To construct B, test each element x of A and check whether x + 1 is also an element of A. For x = 2, x + 1 = 3, which belongs to A, so 2 ∈ B. For 3, 5, 7, and 11, the successors 4, 6, 8, and 12 are not in A. Hence B = {2}. Removing B from A leaves A \ B = {3, 5, 7, 11}.
Frequently asked questions
What is the correct answer to this question?
{3, 5, 7, 11}
Why is this the correct answer?
To construct B, test each element x of A and check whether x + 1 is also an element of A. For x = 2, x + 1 = 3, which belongs to A, so 2 ∈ B. For 3, 5, 7, and 11, the successors 4, 6, 8, and 12 are not in A. Hence B = {2}. Removing B from A leaves A \ B = {3, 5, 7, 11}.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
Advertisement