Advertisements
Advertisements
प्रश्न
Determine the domain and range of the relations:
(i) R = {(a, b) : a ∈ N, a < 5, b = 4}
Advertisements
उत्तर
(i) R = {(a, b) : a ∈ N, a < 5, b = 4}
We have:
a = 1, 2, 3, 4
b = 4
R = {(1, 4), (2, 4), (3, 4), (4, 4)}
Domain (R) = {1, 2, 3, 4}
Range (R) = {4}
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 R be the relation on Z defined by R = {(a, b): a, b ∈ Z, a – b is an integer}. Find the domain and range of R.
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:
(iii) R is a relation from {11, 12, 13} to (8, 10, 12] defined by y = x − 3.
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 R be a relation from N to N defined by R = {(a, b) : a, b ∈ N and a = b2}. Is the statement true?
(a, b) ∈ R implies (b, a) ∈ R
Justify your answer in case.
The adjacent figure shows a relationship between the sets P and Q. Write this relation in (i) set builder form (ii) roster form. What is its domain and range?
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.
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.
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 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 =
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
A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?
Let R be a relation on N defined by x + 2y = 8. The domain of R is
R is a relation from [11, 12, 13] to [8, 10, 12] defined by y = x − 3. Then, R−1 is
Let R be a relation from a set A to a set B, then
If R is a relation on a finite set having n elements, then the number of relations on A 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
Write the relation in the Roster Form. State its domain and range
R2 = `{("a", 1/"a") // 0 < "a" ≤ 5, "a" ∈ "N"}`
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}
Write the relation in the Roster Form. State its domain and range
R7 = {(a, b)/a, b ∈ N, a + b = 6}
Select the correct answer from given alternative.
If (x, y) ∈ R × R, then xy = x2 is a relation which 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
R4 = {(4, 2), (2, 6), (5, 1), (2, 4)}
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:
R = {1, 2, 3} → {1, 2, 3} given by R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)} Check if R is symmentric
Answer the following:
Show that the relation R in the set A = {1, 2, 3, 4, 5} Given by R = {(a, b)/|a − b| is even} is an equivalence relation.
Discuss the following relation for reflexivity, symmetricity and transitivity:
Let P denote the set of all straight lines in a plane. The relation R defined by “lRm if l is perpendicular to m”
Discuss the following relation for reflexivity, symmetricity and transitivity:
Let A be the set consisting of all the members of a family. The relation R defined by “aRb if a is not a sister of b”
Discuss the following relation for reflexivity, symmetricity and transitivity:
On the set of natural numbers the relation R defined by “xRy if x + 2y = 1”
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 equivalence
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 transitive
Let A = {a, b, c}. What is the equivalence relation of smallest cardinality on A? What is the equivalence relation of largest cardinality on A?
In the set Z of integers, define mRn if m − n is divisible by 7. Prove that R is an equivalence relation
Choose the correct alternative:
Let R be the universal relation on a set X with more than one element. Then R is
Choose the correct alternative:
The rule f(x) = x2 is a bijection if the domain and the co-domain are given by
If R2 = {(x, y) | x and y are integers and x2 + y2 = 64} is a relation. Then find R2.
Is the given relation a function? Give reasons for your answer.
f = {(x, x) | x is a real number}
