Class 11 • Maths • Chapter 2
Relations and Functions
True & False Quiz
Map the domain. Rule the range.
✓True
✗False
25
Questions
|
Ch.2
Chapter
|
XI
Class
Why True & False for Relations and Functions?
How this format sharpens your conceptual clarity
🔵 Functions are the language of mathematics and science — every physical law and formula is a function.
✅ Distinguishing T/F about domain, range, and mapping types directly impacts JEE/CBSE scores in this high-weightage chapter.
🎯 Classic trap: every relation is a function (FALSE); every function is a relation (TRUE).
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The empty set is a subset of every set.
Q 2
Every relation from a set \(A\) to a set \(B\) is a function.
Q 3
A function can assign the same image to more than one element of its domain.
Q 4
The domain of a function is the set of all possible output values.
Q 5
The range of a function is always a subset of its codomain.
Q 6
A relation on a set is reflexive if every element is related to itself.
Q 7
A symmetric relation must be reflexive.
Q 8
A function must be one-to-one to be valid.
Q 9
A relation that is reflexive and symmetric need not be transitive.
Q 10
The identity relation on a set is an equivalence relation.
Q 11
Every equivalence relation partitions the underlying set.
Q 12
If a function is one-to-one, then its inverse relation is a function.
Q 13
A function with equal-sized finite domain and codomain must be bijective.
Q 14
If \(f(x) = |x|\) is defined on the domain \([0,\infty)\), then f is one-to-one.
Q 15
The composition of two functions is always commutative.
Q 16
A surjective function may map more than one domain element to the same codomain element.
Q 17
If \( f \circ g \) is one-to-one, then \( g \) must be one-to-one.
Q 18
If \( f \circ g \) is onto, then \( f \) must be onto.
Q 19
A relation that is symmetric and transitive need not be reflexive.
Q 20
Two functions having the same domain and range are necessarily equal.
Q 21
The inverse of a bijective function is also bijective.
Q 22
If \( f: A \to B \) and \( g: B \to C \) are bijections, then \( g \circ f \) is a bijection.
Q 23
A relation on a set having exactly one equivalence class is the universal relation.
Q 24
If \( f(x) = x^2 \) with domain \( \mathbb{R} \), then \( f^{-1} \) exists as a function.
Q 25
For finite sets A and B, a bijection from A to B exists if and only if |A| = |B|.
Key Takeaways — Relations and Functions
Core facts for CBSE Boards & JEE
1
Every function is a relation — but NOT every relation is a function.
2
A function maps each domain element to EXACTLY ONE codomain element.
3
Range ⊆ Codomain — range equals codomain only for onto (surjective) functions.
4
If n(A)=m and n(B)=n, then n(A×B)=mn (Cartesian product).
5
An identity function f(x)=x is always one-one and onto (bijection).
6
Domain of f(x)=√(x−a) is [a,∞); domain of 1/(x−a) is ℝ−{a}.