Sample QuestionsRelations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If $R$ is a relation on a finite set having $n$ elements, then the number of relations on $A$ is:
- A
$2^{\text{n}}$
- ✓
$2^{\text{n}^2}$
- C
$\text{n}^2$
- D
$\text{n}^\text{n}$
Answer: B.
View full solution →If $R$ is a relation from a finite set $A$ having m elements of a finite set $B$ having $n$ elements, then the number of relations from $A$ to $B$ is:
- ✓
$2^{mn}$
- B
$2^{mn} - 1$
- C
$2mn$
- D
$m^n$
Answer: A.
View full solution →If the set $A$ has $p$ elements, $B$ has $q$ elements, then the number of elements in $A \times B$ is:
- A
$p + q$
- B
$p + q + 1$
- ✓
$pq$
- D
$p^2$
Answer: C.
View full solution →Let $R$ be a relation from a set $A$ to a set $B,$ then :
- A
$\text{R}=\text{A}\cup\text{B}$
- B
$\text{R}=\text{A}\cap\text{B}$
- ✓
$\text{R}\subseteq\text{A}\times\text{B}$
- D
$\text{R}\subseteq\text{B}\times\text{A}$
Answer: C.
View full solution →If $\text{R}=\{(\text{x, y}):\text{x, y}\in\text{Z},\text{ x}^2+\text{y}^2\leq4\}$ is a relation on $Z,$ then the domain of $R$ is:
- A
$\{0, 1, 2\}$
- B
$\{0, -1, -2\}$
- ✓
$\{-2, -1, 0, 1, 2\}$
- D
Answer: C.
View full solution →Let A = {1, 2, 3} and $\text{R}=\{(\text{a, b}):|\text{a}^2-\text{b}^2|\leq5,\text{a, b}\in\text{A}\}.$ Then write R as set of ordered pairs.
View full solution →If n(A) = 3, n(B) = 4, then write n(A × A × B).
If $\text{R}=\{(\text{x, y}):\text{x, y}\in\text{W},2\text{x}+\text{y}=8\},$ then write the domain and range of R.
View full solution →If $\text{R}=\{(\text{x, y}):\text{x},\text{ y}\in\text{Z},\text{ x}^2+\text{y}^2\leq4\}$ is a relation defined on the set Z of integers, then write domain of R.
View full solution →Let A = {1, 2, 3, 5}, B = {4, 6, 9} and R be a relation from A to B defined by R = {(x, y) : x - y is odd}. Write R in roster form.
Find the inverse relation $R ^{-1}$ in the following case:
$R$ is a relation from $\{11,12,13\}$ to $(8,10,12\}$ defined by $y=x-3$.
View full solution →Determine the domain and range of the following relations:
$\text{R}=\{(\text{a, b}):\text{a}\in\text{N},\text{a}<5,\text{b}=4\}$
View full solution →Define a relation R on the set N of natural number by R = $\{$(x, y): y = x + 5}, x is a natural number less than 4, $\text{x, y}\in\text{N}\}$
Depict this relationship using:
- Roster form.
- An arrow diagram. Write down the domain and range or R.
View full solution →Let A be the set of first five natural numbers and let R be a relation on A defined as follows:
$(\text{x, y})\in\text{R}\Leftrightarrow\text{x}\leq\text{y}$
Express $R$ and $R^{-1}$ as sets of ordered pairs. Determine also:
- The domain of $R^{-1}$
- The range of $R.$
View full solution →Let R be a relation on N × N defined by:
$(\text{a, b})\text{ R }(\text{c, d})\Leftrightarrow\text{a}+\text{d}=\text{b}+\text{c}$ for all $(\text{a, b}),(\text{c, d})\in\text{N}\times\text{N}$
Show that:
$(\text{a},\text{b})\text{ R }(\text{c, d})\Rightarrow(\text{c},\text{d})\text{ R (a, b)}$ for all $\text{(a, b)(c, d)}\in\text{N}\times\text{N}$
View full solution →If A = {1, 2, 4} and B = {1, 2, 3}, represent following sets graphically:
B × A
Determine the domain and range of the relation $R$ defined by:
$R=\left\{\left(x, x^3\right): x\right.$ is a prime number less than 10$\}$
View full solution →If A = {1, 2, 3} and B = {2, 4}, what are A × B, B × A, A × A, B × B and $(\text{A}\times\text{B})\cap(\text{B}\times\text{A})?$
View full solution →Let R be a relation from N to N defined by $\text{R}=\{(\text{a, b}):\text{a, b}\in\text{N and a}=\text{b}^2\}.$ Are the following statement true?
$(\text{a, b})\in\text{R and (b, c)}\in\text{R}\Rightarrow \text{(a, c)}\in\text{R}$
View full solution →Write the following relation as the sets of ordered pairs:
A relation R on the set {1, 2, 3, 4, 5, 6, 7}defined by $(\text{x, y})\in \text{R}\Leftrightarrow\text{x}$ is relatively prime to y.
View full solution →Prove that:
$(\text{A}\cap\text{B})\times\text{C}=(\text{A}\times\text{C})\cap(\text{B}\times\text{C})$
View full solution →Prove that:
$(\text{A}\cup\text{B})\times\text{C}=(\text{A}\times\text{C})\cup(\text{B}\times\text{C})$
View full solution →If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
$(\text{A}\times\text{B})\cap(\text{A}\times\text{C})$
View full solution →If $\text{A}\times\text{b}\subseteq\text{C}\times\text{D and A}\times\text{B}=\phi,$ prove that $\text{A}\subseteq\text{C and B}\subseteq\text{D}$
View full solution →If A = {1, 2, 3}, B = {3, 4} and C = {4, 5, 6}, find
$\text{A}\times(\text{B}\cup\text{C})$
View full solution →