Sample QuestionsRelations questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
R is a relation from {11, 12, 13} to {8, 10, 12} defined by y = x - 3. Then, R
-1 is:
-
{(8, 11), (10, 13)}
-
{(11, 8), (13, 10)}
-
{(10, 13), (8, 11), (12, 10)}
-
none of these.
Let R be a relation on N defined by x + 2y = 8. The domain of R is:
- {2, 4, 8}
- {2, 4, 6, 8}
- {2, 4, 6}
- {1, 2, 3, 4}
Let R be a relation from a set A to a set B, then:
- $\text{R}=\text{A}\cup\text{B}$
- $\text{R}=\text{A}\cap\text{B}$
- $\text{R}\subseteq\text{A}\times\text{B}$
- $\text{R}\subseteq\text{B}\times\text{A}$
View full solution →Let A = {1, 2, 3}, B = {1, 3, 5}. If relation R from A to B is given by = {(1, 3), (2, 5), (3, 3)}, Then R
-1 is:
- {(3, 3), (3, 1), (5, 2)}
- {(1, 3), (2, 5), (3, 3)}
- {(1, 3), (5, 2)}
- none of these.
If the set A has p elements, B has q elements, then the number of elements in A × B is:
- p + q
- p + q + 1
- pq
- p2
Let $\text{R}=\{(\text{x, y}):\text{x, y}\in\text{Z},\text{y}=2\text{x}-4\}.$ If (a, -2) and $(4,\text{b}^2)\in\text{R},$ then write the values of a and b.
View full solution →Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, write A and B.
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 →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.
If R is a relation from set A = {11, 12, 13} to set B = {8, 10, 12} defined by y = x - 3, then write R-1
Let R be the relation on Z defined by:
$\text{R}=\{(\text{a, b}):\text{a},\text{b}\in\text{Z, a}-\text{b is an integer\}}$
Find the domain and 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 →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:
$(\text{a},\text{b})\text{ R }(\text{a, b})\text{ for all }(\text{a, b})\in\text{N}\times\text{N}$
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?
$(\text{a, b}):\text{R }\text{for all a}\in\text{N}$
View full solution →Let R be a relation in N defined by $\text{x, y}\in\text{R}\Leftrightarrow\text{x}+2\text{y}=8.$ Express R and R−1 as sets of ordered pairs.
View full solution →Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.
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 →Write the following relation as the sets of ordered pairs:
A relation R on the set {0, 1, 2, ....., 10} defined by 2x + 3y = 12.
Write the following relation as the sets of ordered pairs:
A relation R from the set {2, 3, 4, 5, 6} to the set {1, 2, 3} defined by x = 2y.
Write the following relation as the sets of ordered pairs:
A relation R from a set A = {5, 6, 7, 8} to the set B = {10, 12, 15, 16, 18} defined by $\text{x, y}\in\text{R}\Leftrightarrow\text{x}$ divides y.
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 →Prove that:
$(\text{A}\cap\text{B})\times\text{C}=(\text{A}\times\text{C})\cap(\text{B}\times\text{C})$
View full solution →Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that:
$\text{A}\times\text{C}\subset\text{B}\times\text{D}$
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 = {4}, C = {5}, then verify that:
$\text{A}\times(\text{B}-\text{C})=(\text{A}\times\text{B})-(\text{A}\times\text{C})$
View full solution →