Sets Operations

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If A = {x : x² - 5x + 6 = 0} and B = {x : x² - 3x + 2 = 0}, then A ∩ B equals

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{1}

{2}

{3}

{1, 2}

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Subject: mathematics
Chapter: sets, relations and functions
Topic: sets operations
Difficulty: Medium
Year: 2025

Solution

Correct Answer:

{2}

Solve for Set A: $x^{2} - 5 x + 6 = 0$ .
- Factorizing: $(x - 2) (x - 3) = 0 ⟹ x \in {2, 3}$ .
Solve for Set B: $x^{2} - 3 x + 2 = 0$ .
- Factorizing: $(x - 1) (x - 2) = 0 ⟹ x \in {1, 2}$ .
Find Intersection: Elements common to both sets.
- $A \cap B = {2, 3} \cap {1, 2} = {2}$ .
Result: The intersection is the singleton set {2}.

This medium difficulty mathematics question is from the chapter sets, relations and functions, covering the topic of sets operations. It appeared in the 2025 exam.

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