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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 5

If A = {x ∈ ℤ : x² − 5x + 6 = 0} and B = {2, 3}, which statement is correct?

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Answer and explanation

Correct answer: A = B

Factor the quadratic equation: x² − 5x + 6 = (x − 2)(x − 3) = 0. Hence x = 2 or x = 3. Both values are integers, so the set defined by the condition is A = {2, 3}. Since B is also {2, 3}, the two sets contain exactly the same elements and therefore A = B. The order of elements does not matter in a set.

Tags

setsequal setsquadratic equationsolution setThe Empty SetFinite and Infinite Setsthe empty set finite and infinite sets equal setsMathematicsClass 10 MCQ

Frequently asked questions

What is the correct answer to this question?

A = B

Why is this the correct answer?

Factor the quadratic equation: x² − 5x + 6 = (x − 2)(x − 3) = 0. Hence x = 2 or x = 3. Both values are integers, so the set defined by the condition is A = {2, 3}. Since B is also {2, 3}, the two sets contain exactly the same elements and therefore A = B. The order of elements does not matter in a set.

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.

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