If A = {x : x² − 5x + 6 = 0} and B = {2, 3}, which relation is correct?
Answer and explanation
Correct answer: A = B
Solve the defining equation for A by factoring: x² − 5x + 6 = (x − 2)(x − 3) = 0. Thus x = 2 or x = 3, so A = {2, 3}. Since B is also {2, 3}, the two sets contain exactly the same elements and therefore A = B. The proper-subset options are false because neither set is strictly smaller, and their intersection is {2,3}, not empty.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
Solve the defining equation for A by factoring: x² − 5x + 6 = (x − 2)(x − 3) = 0. Thus x = 2 or x = 3, so A = {2, 3}. Since B is also {2, 3}, the two sets contain exactly the same elements and therefore A = B. The proper-subset options are false because neither set is strictly smaller, and their intersection is {2,3}, not empty.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Equal sets and Subsets.
