Class 12 • mathematics • Chapter 1
relations and functions
True & False Quiz
Map. Compose. Invert.
✓True
✗False
25
Questions
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Ch.1
Chapter
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XII
Class
Why True & False for relations and functions?
How this format sharpens your conceptual clarity
🔵 Relations and Functions opens Class XII Maths and quietly underpins composition and invertibility questions across the paper.
✅ T/F sharply tests reflexive/symmetric/transitive properties and one-one/onto distinctions — a CBSE Board favourite.
🎯 Classic trap: every function is a relation (TRUE), but a relation is a function only if every domain element maps to exactly one image.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
A relation from a set \(A\) to a set \(B\) is any subset of \(A\times B\).
Q 2
If \(|A|=3\) and \(|B|=4\), then \(|A\times B|=7\).
Q 3
Every function is a relation, but every relation is not necessarily a function.
Q 4
The number of relations from a set of 2 elements to a set of 3 elements is \(2^6=64\).
Q 5
The Cartesian product \(A\times B\) is always equal to \(B\times A\).
Q 6
In a function, every element of the domain has exactly one image.
Q 7
The range of a function is always equal to its codomain.
Q 8
The identity function on a set \(A\) is defined by \(f(x)=x\).
Q 9
A constant function is always one-one.
Q 10
A one-one function maps distinct elements of the domain to distinct elements of the codomain.
Q 11
An onto function covers every element of the codomain.
Q 12
Every bijective function has an inverse.
Q 13
The composition of two functions is always commutative.
Q 14
Function composition is associative.
Q 15
The relation \(aRb\iff a=b\) is an equivalence relation.
Q 16
A reflexive relation must contain every ordered pair in \(A\times A\).
Q 17
If a relation is symmetric, then \((a,b)\in R\) implies \((b,a)\in R\).
Q 18
A transitive relation satisfies: if \((a,b)\in R\) and \((b,c)\in R\), then \((a,c)\in R\).
Q 19
A relation that is reflexive and symmetric is always an equivalence relation.
Q 20
The function \(f(x)=x^2\) on \(\mathbb{R}\) is one-one.
Q 21
The function \(f(x)=x^3\) on \(\mathbb{R}\) is bijective.
Q 22
The domain of \(f(x)=\dfrac{1}{x}\) is \(\mathbb{R}\).
Q 23
The range of \(f(x)=x^2\) on \(\mathbb{R}\) is \(\{x\in\mathbb{R}:x\ge0\}\).
Q 24
The number of functions from a set of 3 elements to a set of 2 elements is \(2^3=8\).
Q 25
If \(f:A\to B\) is invertible, then \(f^{-1}\circ f=I_A\) and \(f\circ f^{-1}=I_B\).
Key Takeaways — relations and functions
Core facts for CBSE Boards & JEE
1
A relation R is an equivalence relation only if it is reflexive, symmetric AND transitive — all three, together.
2
A function is one-one (injective) if distinct inputs always give distinct outputs; onto (surjective) if every codomain element has a preimage.
3
A function is invertible if and only if it is bijective (both one-one and onto).
4
Composition of functions is associative: (f∘g)∘h = f∘(g∘h), but generally NOT commutative.
5
If f is invertible with inverse g, then f∘g = g∘f = identity function.
6
The identity relation on a set is always an equivalence relation, but the empty relation is reflexive only on the empty set.