Chapter Exam

Chapter 2 - Relations and Functions — Online MCQ Test

Q: What is a relation in mathematics?

Answer: A. A subset of the Cartesian product of two sets — A relation is formally defined as a subset of the Cartesian product A × B, where A and B are two sets.

Q: If A = {1, 2, 3} and B = {a, b}, how many elements are in A × B?

Answer: C. 6 — The Cartesian product A × B has |A| × |B| = 3 × 2 = 6 elements.

Q: If f(x) = x² and g(x) = x + 1, what is (f ∘ g)(2)?

Answer: B. 9 — (f ∘ g)(2) = f(g(2)) = f(3) = 3² = 9. First apply g, then apply f to the result.

Q: A relation that is reflexive, antisymmetric, and transitive is called a _____.

Answer: B. Partial order relation — A partial order (or partial ordering) is a relation that is reflexive, antisymmetric, and transitive.

MATHS · CLASS 11 FIRST PUC · Karnataka State Board

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Chapter 2 - Relations and Functions — Important Questions & Answers (FAQ)

Frequently asked questions from Karnataka State Board CLASS 11 FIRST PUC MATHS — Chapter 2 - Relations and Functions, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is a relation in mathematics?

A. A subset of the Cartesian product of two sets ✓
B. A function that maps every element to itself
C. A set of ordered pairs with no specific rule
D. An equivalence between two algebraic expressions

Answer: A. A subset of the Cartesian product of two sets
A relation is formally defined as a subset of the Cartesian product A × B, where A and B are two sets.

If A = {1, 2, 3} and B = {a, b}, how many elements are in A × B?

A. 3
B. 5
C. 6 ✓
D. 2

Answer: C. 6
The Cartesian product A × B has |A| × |B| = 3 × 2 = 6 elements.

If f(x) = x² and g(x) = x + 1, what is (f ∘ g)(2)?

A. 5
B. 9 ✓
C. 8
D. 7

Answer: B. 9
(f ∘ g)(2) = f(g(2)) = f(3) = 3² = 9. First apply g, then apply f to the result.

A relation that is reflexive, antisymmetric, and transitive is called a _____.

A. Equivalence relation
B. Partial order relation ✓
C. Congruence relation
D. Total relation

Answer: B. Partial order relation
A partial order (or partial ordering) is a relation that is reflexive, antisymmetric, and transitive.

Consider the function f: Z → Z defined by f(n) = n/2 if n is even, and f(n) = (n+1)/2 if n is odd. Is f surjective?

A. Yes, f is surjective because every integer has a pre-image ✓
B. No, because f is not defined for all integers
C. Yes, f is surjective because it covers all even integers
D. No, because negative integers cannot be in the range

Answer: A. Yes, f is surjective because every integer has a pre-image
For any integer m in Z, we can find an integer n such that f(n) = m. For example, if m ≥ 0, take n = 2m (even), then f(2m) = m. Thus f is onto (surjective).