If $A=\{a, b, c\}$, The total no. of distinct relations in $A \times A$ is
- A3
- B9
- C8
- ✓29
Answer: D.
View full solution →Question types
Sets and Relations question types
102 questions across 6 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
102
Questions
6
Question groups
5
Question types
01
MCQ
10 Q→02Solve the following Question.(1 Marks)
54 Q→03Solve the Following Question.(2 Marks)
23 Q→04Solve the Following Question.(3 Marks)
12 Q→05Solve the Following Question.(4 Marks)
2 Q→06Solve the Following Question.(5 Marks)
1 Q→Sample Questions
Sets and Relations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $(x, y) \in N \times N$, then $x y=x^2$ is a relation that is
- ASymmetric
- BReflexive
- CTransitive
- ✓Equivalence
Answer: D.
View full solution →A relation between $A$ and $B$ is
- Aonly $A \times B$
- BAn Universal set of $A \times B$
- CAn equivalent set of $A \times B$
- ✓A subset of $A \times B$
Answer: D.
View full solution →The relation " $>$ " in the set of $N$ (Natural number) is
- ASymmetric
- BReflexive
- ✓Transitive
- DEquivalent relation
Answer: C.
View full solution →Let $R$ be a relation on the set $N$ be defied by $\{(x, y) / x, y \in N, 2 x+y=41\}$ Then $R$ is
- AReflexive
- BSymmetric
- CTransitive
- ✓None of these
Answer: D.
View full solution →If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1,4, 7,10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12}. Write down the sets. B ∩ C
If U = {x/x ∈ N, 1 ≤ x ≤ 12}, A = {1,4, 7,10}, B = {2, 4, 6, 7, 11}, C = {3, 5, 8, 9, 12}. Write down the sets. A ∪ B
Write down the following sets in set builder form:
{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
{Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
Write down the following sets in set builder form:
{a, e, i, o, u}
{a, e, i, o, u}
Write down the following sets in set builder form:
{10, 20, 30, 40, 50}
Find R : A → A when A = {1, 2, 3, 4} such that
R = {(a, b) / |a – b| ≥ 0}
R = {(a, b) / |a – b| ≥ 0}
Find R : A → A when A = {1, 2, 3, 4} such that
(i) R = {(a, b) / a – b = 10}
Determine the domain and range of the following relations.
R = {(a, b) / b = |a – 1|, a ∈ Z, |a| < 3}
If A = {-1, 1}, find A × A × A.
If A = {1, 2, 3} and B = {2, 4}, state the elements of A × A, A × B, B × A, B × B, (A × B) ∩ (B × A).
Show that the following are equivalence relations:
R in A = (x ∈ N/x ≤ 10} given by R = {(a, b) | a = b}
Show that the following are equivalence relations:
R in A = {x ∈ Z | 0 ≤ x ≤ 12} given by R = {(a, b) / |a – b| is a multiple of 4}
Show that the following are equivalence relations:
R in A is set of all books given by R = {(x, y) / x and y have same number of pages}
Show that the relation R in the set A = {1, 2, 3, 4, 5} Given by R = {(a, b) / |a – b| is even} is an equivalence relation.
Check if R : Z → Z, R = {(a, b) | 2 divides a – b} is an equivalence relation.
A college awarded 38 medals in volleyball, 15 in football, and 20 in basketball. The medals were awarded to a total of 58 players and only 3 players got medals in all three sports. How many received medals in exactly two of the three sports?
Describe the following sets in Set-Builder form:
View full solution →(i) {0} (ii) {0, ±1, ±2, ±3}
(iii) $\left\{\frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, \frac{7}{50}\right\}$
(iv) {0, -1, 2, -3, 4, -5, 6,…}
Identify which of the following relations are reflexive, symmetric, and transitive.
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