If A = {2, 3, 4, 5} and B = {4, 5, 6, 7}, which statement is false?
Answer and explanation
Correct answer: B \ A = {2, 3}
The common elements of A and B are 4 and 5, so A ∩ B = {4, 5}. Combining all distinct elements gives A ∪ B = {2, 3, 4, 5, 6, 7}. Removing B’s elements from A leaves A \ B = {2, 3}. However, B \ A means elements in B but not in A; these are 6 and 7, so B \ A = {6, 7}, not {2, 3}. Therefore statement D is false.
Frequently asked questions
What is the correct answer to this question?
B \ A = {2, 3}
Why is this the correct answer?
The common elements of A and B are 4 and 5, so A ∩ B = {4, 5}. Combining all distinct elements gives A ∪ B = {2, 3, 4, 5, 6, 7}. Removing B’s elements from A leaves A \ B = {2, 3}. However, B \ A means elements in B but not in A; these are 6 and 7, so B \ A = {6, 7}, not {2, 3}. Therefore statement D is false.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
