Advertisements
Advertisements
Question
Answer the following:
Determine the domain and range of the following relation.
R = {(a, b)/a ∈ N, a < 5, b = 4}
Advertisements
Solution
R = {(a, b)/a ∈ N, a < 5, b = 4}
Domain of R = {a/a ∈ N, a < 5}
={1, 2, 3, 4}
Range of R = {b/b = 4}
= {4}
APPEARS IN
RELATED QUESTIONS
The given figure shows a relationship between the sets P and Q. Write this relation
- in set-builder form.
- in roster form.
What is its domain and range?
Write the relation R = {(x, x3): x is a prime number less than 10} in roster form.
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 relation from A to B
Justify your answer in case.
Find the inverse relation R−1 in each of the cases:
(i) R = {(1, 2), (1, 3), (2, 3), (3, 2), (5, 6)}
Determine the domain and range of the relations:
(i) R = {(a, b) : a ∈ N, a < 5, b = 4}
Let A = (x, y, z) and B = (a, b). Find the total number of relations from A into B.
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?
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
(iii) (a, b) R (c, d) and (c, d) R (e, f) ⇒ (a, b) R (e, f) for all (a, b), (c, d), (e, f) ∈ N × N
If A = {1, 2, 4}, B = {2, 4, 5} and C = {2, 5}, write (A − C) × (B − C).
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.
If A = [1, 3, 5] and B = [2, 4], list of elements of R, if
R = {(x, y) : x, y ∈ A × B and x > y}
If R = [(x, y) : x, y ∈ W, 2x + y = 8], then write the domain and range of R.
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 − yis odd}. Write R in roster form.
If R = {(x, y) : x, y ∈ Z, x2 + y2 ≤ 4} is a relation on Z, then the domain of R is ______.
A relation R is defined from [2, 3, 4, 5] to [3, 6, 7, 10] by : x R y ⇔ x is relatively prime to y. Then, domain of R is
A relation ϕ from C to R is defined by x ϕ y ⇔ |x| = y. Which one is correct?
R is a relation from [11, 12, 13] to [8, 10, 12] defined by y = x − 3. Then, R−1 is
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
R1 = {(a, a2)/a is prime number less than 15}
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
R7 = {(a, b)/a, b ∈ N, a + b = 6}
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 reflexive
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 transitive
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}
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 P be the set of all triangles in a plane and R be the relation defined on P as aRb if a is similar to b. Prove that R is an equivalence relation
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 symmetric
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:
The relation R defined on a set A = {0, −1, 1, 2} by xRy if |x2 + y2| ≤ 2, then which one 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 following relation a function? Justify your answer
R2 = {(x, |x |) | x is a real number}
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 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 ______.
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.
