Sample QuestionsRelation 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:
- ✓
$2^{\mathrm{mn}}$
- B
$2^{m n}-1$
- C
$2 mn$
- D
$\mathrm{m}^n$
Answer: A.
View full solution →If the set A has p elements, B has q elements, then the number of elements in A × B is:
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:
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 = {$(x, x^3)$: x 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 →