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Relations Maths - Relations

Uttarakhand Board (UBSE) - STD 12 Science - Maths (Uttarakhand - English Medium). 114 questions in this chapter.

Question types

Relations question types

114 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

114
Questions
4
Question groups
5
Question types
Sample Questions

Relations questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The relation S defined on the set R of all real number by the rule aSb iff a ≥ b is:
  • A
    An equivalence relation.
  • ✓
    Reflexive, transitive but not symmetric.
  • C
    Symmetric, transitive but not reflexive.
  • D
    Neither transitive nor reflexive but symmetric.

Answer: B.

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Q 2M.C.Q (1 Marks)1 Mark
$S$ is a relation over the set $R$ of all real numbers and it is given by $(\text{a, b})\in\text{S}\Leftrightarrow\text{ab}\geq0.$ Then$, S$ is:
  • A
    Symmetric and transitive only.
  • B
    Reflexive and symmetric only.
  • C
    Antisymmetric relation.
  • ✓
    An equivalence relation.

Answer: D.

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Q 3M.C.Q (1 Marks)1 Mark
The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is:
  • A
    Symmetric only.
  • B
    Reflexive only.
  • ✓
    An equivalence relation.
  • D
    Transitive only.

Answer: C.

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Q 4M.C.Q (1 Marks)1 Mark
Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if l is perpendicular to m for all l, m ∈ L. Then, R is:
  • A
    Reflexive.
  • ✓
    Symmetric.
  • C
    Transitive.
  • D
    None of these.

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark
In the set Z of all integers, which of the following relation R is not an equivalence relation?
  • ✓
    xRy : if $\text{x}\leq\text{y}$
  • B
    xRy : if x = y
  • C
    xRy : if x - y is an even integer
  • D
    xRy : if $\text{x}\equiv\text{y}\ (\text{mod 3})$

Answer: A.

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Q 123 Marks Question3 Marks
Test whether the following relations $R_2$ are:
  1. Reflexive.
  2. Symmetric.
  3. Transitive.
$R_2​​​​​​​$​​​​​​​ on Z defined by $(\text{a, b})\in\text{R}_2\Leftrightarrow\ |\text{a}-\text{b}|\leq5$
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Q 133 Marks Question3 Marks
Let $A = {1, 2, 3},$ and let $R_1 = {(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3)}$. Find whether or not the relations $R_1$ on $A$ is:
  1. Reflexive.
  2. Symmetric.
  3. Transitive.
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Q 143 Marks Question3 Marks
The following relation are defined on the set of real numbers.
aRb if $1 + ab > 0$
Find whether these relation are reflexive, symmetric or transitive.
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Q 153 Marks Question3 Marks
Let A$ = {1, 2, 3}, $and let $R_3 = {(1, 3), (3, 3)}$. Find whether or not the relations $R_3$ on $A$ is:
  1. Reflexive.
  2. Symmetric.
  3. Transitive.
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Q 165 Marks Questions5 Marks
Show that the relation $R,$ defined on the set $A$ of all polygons as $R = \{(P_1, P_2): P_1$ and $P_2$ have same number of sides$\},$ is an equivalence relation. What is the set of all elements in $A$ related to the right angle triangle $T$ with sides $3, 4$ and $5?$
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Q 175 Marks Questions5 Marks
Let $Z$ be the set of all integers and $Z_0$ be the set of all non-zero integers. Let a relation $R$ on $Z \times Z_0$ be defined as $(a, b)R(c, d) ⇔ ad = bc$ for all $(a, b), (c, d) \in Z \times Z_0,$ Prove that $R$ is an equivalence relation on $Z \times Z_0.$
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Q 185 Marks Questions5 Marks
Let R be the relation defined on the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b): both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset {1, 3, 5, 7} are related to each other and all the elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7} is related to any element of the subset {2, 4, 6}.
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Q 205 Marks Questions5 Marks
Let n be a fixed positive integer. Define a relation R on Z as follows:
$(\text{a, b})\in\text{R}\Leftrightarrow\ \text{a}-\text{b}$ is divisible by n. Show that R is an equivalence relation on Z.
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