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Class 10MathematicsSetsThe Empty Set, Finite and Infinite Sets, Equal SetsMediumLevel 6

If D = {x : x ∈ ℕ, x² - 5x + 6 = 0} and E = {2, 3}, which statement is correct?

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Answer and explanation

Correct answer: D = E

Factor the quadratic equation: x² - 5x + 6 = (x - 2)(x - 3) = 0. Thus x = 2 or x = 3. Both values are natural numbers, so D = {2, 3}. Since E is also {2, 3}, the two sets contain exactly the same elements and are equal. The order or form in which elements are written does not affect set equality.

Tags

setsequal setsquadratic equationfinite 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?

D = E

Why is this the correct answer?

Factor the quadratic equation: x² - 5x + 6 = (x - 2)(x - 3) = 0. Thus x = 2 or x = 3. Both values are natural numbers, so D = {2, 3}. Since E is also {2, 3}, the two sets contain exactly the same elements and are equal. The order or form in which elements are written does not affect set equality.

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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