Let A = {x ∈ Z : x² − 4x + 3 = 0} and B = {1, 3}. Which relation is correct?
Answer and explanation
Correct answer: A = B
To determine A, factor the quadratic equation: x² − 4x + 3 = (x − 1)(x − 3) = 0. Therefore x = 1 or x = 3. Both solutions are integers, so A = {1, 3}. Since B is also {1, 3}, the two sets contain exactly the same elements and A = B. Equal sets do not depend on the order in which their elements are written. Thus neither set is a proper subset of the other, and their intersection is not empty.
Frequently asked questions
What is the correct answer to this question?
A = B
Why is this the correct answer?
To determine A, factor the quadratic equation: x² − 4x + 3 = (x − 1)(x − 3) = 0. Therefore x = 1 or x = 3. Both solutions are integers, so A = {1, 3}. Since B is also {1, 3}, the two sets contain exactly the same elements and A = B. Equal sets do not depend on the order in which their elements are written. Thus neither set is a proper subset of the other, and their intersection is not empty.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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