Advertisements
Advertisements
प्रश्न
Answer the following:
Determine the domain and range of the following relation.
R = {(a, b)/b = |a – 1|, a ∈ Z, IaI < 3}
Advertisements
उत्तर
R = {(a, b)/b = |a – 1|, a ∈ Z, IaI < 3}
Since, a ∈ Z and |a| < 3
∴ a < 3 and a > – 3
∴ – 3 < a < 3
∴ a = – 2, – 1, 0, 1, 2
b = |a – 1|
When a = – 2, b = 3
When a = – 1, b = 2
When a = 0, b = 1
When a = 1, b = 0
When a = 2, b = 1
∴ Domain (R) = {– 2, – 1, 0, 1, 2}
Range (R) = {0, 1, 2, 3}
APPEARS IN
संबंधित प्रश्न
A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y): the difference between x and y is odd; x ∈ A, y ∈ B}. Write R in roster form.
Let A = {x, y, z} and B = {1, 2}. Find the number of relations from A to B.
The relation f is defined by f(x) = `{(x^2,0<=x<=3),(3x,3<=x<=10):}`
The relation g is defined by g(x) = `{(x^2, 0 <= x <= 2),(3x,2<= x <= 10):}`
Show that f is a function and g is not a function.
Find the inverse relation R−1 in each of the cases:
(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}
Let A = [1, 2] and B = [3, 4]. Find the total number of relation from A into B.
Let A = (x, y, z) and B = (a, b). Find the total number of relations from A into B.
Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:
(i) (a, b) R (a, b) for all (a, b) ∈ N × N
Let R be a relation on N × N defined by
(a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N
Show that:
(ii) (a, b) R (c, d) ⇒ (c, d) R (a, b) for all (a, b), (c, d) ∈ N × N
If R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation defined on the set Z of integers, then write domain of R.
If R is a relation on a finite set having n elements, then the number of relations on A is
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 = {6, 8} and B = {1, 3, 5}
Show that R1 = {(a, b)/a ∈ A, b ∈ B, a − b is an even number} is a null relation. R2 = {(a, b)/a ∈ A, b ∈ B, a + b is odd number} is an universal relation
Write the relation in the Roster Form. State its domain and range
R3 = {(x, y)/y = 3x, y∈ {3, 6, 9, 12}, x∈ {1, 2, 3}
Select the correct answer from given alternative
If A = {a, b, c} The total no. of distinct relations in A × A is
Answer the following:
If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range
R2 = {(1, 5), (2, 4), (3, 6)}
Answer the following:
If A = {1, 2, 3}, B = {4, 5, 6} check if the following are relations from A to B. Also write its domain and range
R4 = {(4, 2), (2, 6), (5, 1), (2, 4)}
Answer the following:
Check if R : Z → Z, R = {(a, b)/2 divides a – b} is equivalence relation.
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
R2 = {(–1, 1)}
Let A = {1, 2, 3, 7} and B = {3, 0, –1, 7}, the following is relation from A to B?
R4 = {(7, –1), (0, 3), (3, 3), (0, 7)}
Let A = {1, 2, 3, 4, …, 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A × A. Also, find the domain and range of R
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}
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 ________.
Let X = {a, b, c, d} 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
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 equivalence
On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is reflexive
On the set of natural numbers let R be the relation defined by aRb if 2a + 3b = 30. Write down the relation by listing all the pairs. Check whether it is transitive
Choose the correct alternative:
The rule f(x) = x2 is a bijection if the domain and the co-domain are given by
Find the domain and range of the relation R given by R = {(x, y) : y = `x + 6/x`; where x, y ∈ N and x < 6}.
Given R = {(x, y) : x, y ∈ W, x2 + y2 = 25}. Find the domain and Range of R.
If R1 = {(x, y) | y = 2x + 7, where x ∈ R and – 5 ≤ x ≤ 5} is a relation. Then find the domain and Range of R1.
Is the given relation a function? Give reasons for your answer.
s = {(n, n2) | n is a positive integer}
If R = {(x, y): x, y ∈ Z, x2 + 3y2 ≤ 8} is a relation on the set of integers Z, then the domain of R–1 is ______.
Let f: R `rightarrow` R be defined by f(x) = `x/(1 + x^2), x ∈ R`. Then the range of f is ______.
Let N denote the set of all natural numbers. Define two binary relations on N as R1 = {(x, y) ∈ N × N : 2x + y = 10} and R2 = {(x, y) ∈ N × N : x + 2y = 10}. Then ______.
