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Class 12 Relations and Functions worksheet
CBSE Mathematics. Reflexive, symmetric and transitive relations, equivalence classes, one-one and onto functions, composition, inverses. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
The number of relations on a set with 1 element is:
- 2
- 3
- 1
- 4
Answer
(a) 2
2^(1 × 1) = 2¹
- 2.
The number of bijective functions from a set with 6 elements to itself is:
- 720
- 46,656
- 64
- 36
Answer
(a) 720
6! = 6 × 5 × 4 × 3 × 2 × 1
- 3.
If f(x) = −3x − 2 and g(x) = −2x + 8, then (g ∘ f)(x) is:
- 6x + 12
- 6x − 16
- 6x − 26
- −5x + 6
Answer
(a) 6x + 12
g(f(x)) = −2(−3x − 2) + 8
Section B · short answer
- 4.
Determine whether the relation R = {(1, 1), (1, 4), (2, 2), (3, 2), (3, 3)} on A = {1, 2, 3, 4} is reflexive, symmetric and transitive.
Answer
transitive only
not reflexive: (4, 4) ∉ R; not symmetric: (1, 4) ∈ R but (4, 1) ∉ R; transitive
- 5.
R = {(a, b) : a − b is divisible by 4} is an equivalence relation on A = {0, 1, 2, …, 8}. Find the equivalence class [0].
Answer
{0, 4, 8}
the elements that leave remainder 0 on division by 4
Section C · long answer
- 6.
Show that R = {(a, b) : |a − b| is a multiple of 3} is an equivalence relation on A = {1, 2, …, 12}, and write all its equivalence classes.
Answer
Reflexive: |a − a| = 0 is a multiple of 3. Symmetric: |a − b| = |b − a|. Transitive: a − c = (a − b) + (b − c). Classes: {1, 4, 7, 10}, {2, 5, 8, 11}, {3, 6, 9, 12}
group the numbers by their remainder on division by 3
Fresh sheets for your child
In the app, every Relations and Functions sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
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