Advertisements
Advertisements
प्रश्न
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}
Advertisements
उत्तर
Given:
A = {1, 3, 5} and B = {2, 4}
R = {(x, y) : x, y ∈ A × B and x > y}
A × B = {(1,2),(1,4),(3,2),(3,4),(5,2),(5,4)}
As 3 > 2, 5 > 2 and 5 > 4,
we have R = {(3,2),(5,2),(5,4)}
APPEARS IN
संबंधित प्रश्न
Let A = {1, 2, 3, …, 14}. Define a relation R from A to A by R = {(x, y): 3x – y = 0, where x, y ∈ A}. Write down its domain, codomain and range.
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.
Determine the domain and range of the relation R defined by
(ii) R = {(x, x3) : x is a prime number less than 10}
Let A = (x, y, z) and B = (a, b). Find the total number of relations from A into B.
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.
Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, write A and B
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, 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
If the set A has p elements, B has q elements, then the number of elements in A × B 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 + 1/3, 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
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
R5 = {(x, y)/x + y = 3, x, y∈ {0, 1, 2, 3}
Write the relation in the Roster Form. State its domain and range
R6 = {(a, b)/a ∈ N, a < 6 and b = 4}
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.
A relation between A and B is
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:
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 = {x ∈ N/x ≤ 10} given by R = {(a, b)/a = b}
Let A = {9, 10, 11, 12, 13, 14, 15, 16, 17} and let f : A → N be defined by f(n) = the highest prime factor of n ∈ A. Write f as a set of ordered pairs and find the range of f
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”
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
Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai
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 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 transitive
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
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 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?
Is the given relation a function? Give reasons for your answer.
h = {(4, 6), (3, 9), (– 11, 6), (3, 11)}
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 ______.
