Advertisements
Advertisements
प्रश्न
Let A = [1, 2, 3, ......., 14]. Define a relation on a set A by
R = {(x, y) : 3x − y = 0, where x, y ∈ A}.
Depict this relationship using an arrow diagram. Write down its domain, co-domain and range.
उत्तर
A = [1, 2, 3,..., 14]
R = {(x, y) : 3x − y = 0, where x, y ∈ A}
Or,
R = {(x, y) : 3x = y, where x, y ∈ A}
As
\[3 \times 1 = 3\]
\[3 \times 2 = 6\]
\[3 \times 3 = 9\]
\[3 \times 4 = 12\]
Or,
R = {(1, 3), (2, 6), (3, 9), (4, 12)}
Domain (R) = {1, 2, 3, 4}
Range (R) = {3, 6, 9, 12}
Co-domain (R) = A
APPEARS IN
संबंधित प्रश्न
Define a relation R on the set N of natural numbers by R = {(x, y): y = x + 5, x is a natural number less than 4; x, y ∈ N}. Depict this relationship using roster form. Write down the domain and the range.
Determine the domain and range of the relation R defined by
(i) R = [(x, x + 5): x ∈ (0, 1, 2, 3, 4, 5)]
Determine the domain and range of the relation R defined by
(ii) R = {(x, x3) : x is a prime number less than 10}
Determine the domain and range of the relations:
(ii) \[S = \left\{ \left( a, b \right) : b = \left| a - 1 \right|, a \in Z \text{ and} \left| a \right| \leq 3 \right\}\]
Let A = {a, b}. List all relations on A and find their number.
Let A = [1, 2, 3, 4, 5, 6]. Let R be a relation on A defined by {(a, b) : a, b ∈ A, b is exactly divisible by a}
(i) Writer R in roster form
(ii) Find the domain of R
(ii) Find the range of R.
If R is a relation defined on the set Z of integers by the rule (x, y) ∈ R ⇔ x2 + y2 = 9, then write domain of R.
Let R = [(x, y) : x, y ∈ Z, y = 2x − 4]. If (a, -2) and (4, b2) ∈ R, then write the values of a and b.
If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A − B) × (B − C) is
If R is a relation on the set A = [1, 2, 3, 4, 5, 6, 7, 8, 9] given by x R y ⇔ y = 3x, then R =
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
If A = [1, 2, 3], B = [1, 4, 6, 9] and R is a relation from A to B defined by 'x' is greater than y. The range of R is
Let R be a relation on N defined by x + 2y = 8. The domain of R is
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
If (x − 1, y + 4) = (1, 2) find the values of x and y
If `(x + 1/3, y/3 - 1) = (1/2, 3/2)`, find x and y
If A = {a, b, c}, B = {x, y}, find A × B, B × A, A × A, B × B
Let A = {1, 2, 3, 4), B = {4, 5, 6}, C = {5, 6}. Verify, A × (B ∪ C) = (A × B) ∪ (A × C)
Write the relation in the Roster Form. State its domain and range
R8 = {(a, b)/b = a + 2, a ∈ z, 0 < a < 5}
Identify which of if the following relations are reflexive, symmetric, and transitive.
| Relation | Reflexive | Symmetric | Transitive |
| R = {(a, b) : a, b ∈ Z, a – b is an integer} | |||
| R = {(a, b) : a, b ∈ N, a + b is even} | √ | √ | x |
| R = {(a, b) : a, b ∈ N, a divides b} | |||
| R = {(a, b) : a, b ∈ N, a2 – 4ab + 3b2 = 0} | |||
| R = {(a, b) : a is sister of b and a, b ∈ G = Set of girls} | |||
| R = {(a, b) : Line a is perpendicular to line b in a plane} | |||
| R = {(a, b) : a, b ∈ R, a < b} | |||
| R = {(a, b) : a, b ∈ R, a ≤ b3} |
Select the correct answer from given alternative.
If (x, y) ∈ R × R, then xy = x2 is a relation which is
Answer the following:
Determine the domain and range of the following relation.
R = {(a, b)/b = |a – 1|, a ∈ Z, IaI < 3}
Answer the following:
Find R : A → A when A = {1, 2, 3, 4} such that R = (a, b)/a − b = 10}
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
R3 = {(2, –1), (7, 7), (1, 3)}
A Relation R is given by the set `{(x, y)/y = x + 3, x ∈ {0, 1, 2, 3, 4, 5}}`. Determine its domain and range
Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible
{(x, y) | x = 2y, x ∈ {2, 3, 4, 5}, y ∈ {1, 2, 3, 4}
Represent the given relation by
(a) an arrow diagram
(b) a graph and
(c) a set in roster form, wherever possible
{(x, y) | y = x + 3, x, y are natural numbers < 10}
Multiple Choice Question :
The range of the relation R = {(x, x2) | x is a prime number less than 13} is ________
Multiple Choice Question :
Let n(A) = m and n(B) = n then the total number of non-empty relation that can be defined from A to B is ________.
Find the domain of the function f(x) = `sqrt(1 + sqrt(1 - sqrt(1 - x^2)`
Let A = {a, b, c} and R = {(a, a), (b, b), (a, c)}. Write down the minimum number of ordered pairs to be included to R to make it reflexive
On the set of natural numbers let R be the relation defined by aRb if a + b ≤ 6. Write down the relation by listing all the pairs. Check whether it is symmetric
Choose the correct alternative:
Let R be the set of all real numbers. Consider the following subsets of the plane R × R: S = {(x, y) : y = x + 1 and 0 < x < 2} and T = {(x, y) : x − y is an integer} Then which of the following is true?
Choose the correct alternative:
Let X = {1, 2, 3, 4} and R = {(1, 1), (1, 2), (1, 3), (2, 2), (3, 3), (2, 1), (3, 1), (1, 4), (4, 1)}. Then R is
Is the given relation a function? Give reasons for your answer.
f = {(x, x) | x is a real number}
Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Is the following true?
f is a function from A to B
Justify your answer in case.
