Advertisements
Advertisements
प्रश्न
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
Advertisements
उत्तर
R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)}
Here, (1, 2) ∈ R, but (2, 1) ∉ R.
∴ R is not symmetric.
APPEARS IN
संबंधित प्रश्न
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 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.
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.
If A = [1, 2, 3], B = [4, 5, 6], which of the following are relations from A to B? Give reasons in support of your answer.
(i) [(1, 6), (3, 4), (5, 2)]
(ii) [(1, 5), (2, 6), (3, 4), (3, 6)]
(iii) [(4, 2), (4, 3), (5, 1)]
(iv) A × B.
Let A = (3, 5) and B = (7, 11). Let R = {(a, b) : a ∈ A, b ∈ B, a − b is odd}. Show that R is an empty relation from A into B.
Determine the domain and range of the relation R defined by
(ii) R = {(x, x3) : x is a prime number less than 10}
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 A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A − B) × (B − C) 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 P = {1, 2, 3) and Q = {1, 4}, find sets P × Q and Q × P
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
R1 = {(1, 4), (1, 5), (1, 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
R2 = {(1, 5), (2, 4), (3, 6)}
Answer the following:
Find R : A → A when A = {1, 2, 3, 4} such that R = {(a, b)/|a − b| ≥ 0}
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:
Show that the following is an equivalence relation
R in A is set of all books. given by R = {(x, y)/x and y have same number of pages}
Answer the following:
Show that the following is an equivalence relation
R in A = {x ∈ Z | 0 ≤ x ≤ 12} given by R = {(a, b)/|a − b| is a multiple of 4}
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, 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
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 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 symmetric
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 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 equivalence
Choose the correct alternative:
Let R be the universal relation on a set X with more than one element. Then R is
Is the following relation a function? Justify your answer
R1 = `{(2, 3), (1/2, 0), (2, 7), (-4, 6)}`
Is the following relation a function? Justify your answer
R2 = {(x, |x |) | x is a real number}
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.
Let n(A) = m, and n(B) = n. Then the total number of non-empty relations that can be defined from A to B is ______.
Let f: R `rightarrow` R be defined by f(x) = `x/(1 + x^2), x ∈ R`. Then the range of f is ______.
Let S = {x ∈ R : x ≥ 0 and `2|sqrt(x) - 3| + sqrt(x)(sqrt(x) - 6) + 6 = 0}`. Then S ______.
