Advertisements
Advertisements
Question
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, symmetric and transitive ?
Advertisements
Solution
The relation on A having properties of being symmetric, reflexive and transitive is
R = {(1, 1), (2, 2), (3, 3), (4, 4), (1, 2), (2, 1)}
The relation R is an equivalence relation on A.
APPEARS IN
RELATED QUESTIONS
Let A be the set of all human beings in a town at a particular time. Determine whether the following relation is reflexive, symmetric and transitive:
R = {(x, y) : x is exactly 7 cm taller than y}
Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer.
Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}. Choose the correct answer.
Let A = {x ∈ Z : 0 ≤ x ≤ 12}. Show that R = {(a, b) : a, b ∈ A, |a – b| is divisible by 4}is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]
Let A be the set of all human beings in a town at a particular time. Determine whether the following relation is reflexive, symmetric and transitive:
R = {(x, y) : x and y work at the same place}
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?
Let R be a relation defined on the set of natural numbers N as
R = {(x, y) : x, y ∈ N, 2x + y = 41}
Find the domain and range of R. Also, verify whether R is (i) reflexive, (ii) symmetric (iii) transitive.
Give an example of a relation which is symmetric and transitive but not reflexive?
Give an example of a relation which is transitive but neither reflexive nor symmetric?
Defines a relation on N:
x + 4y = 10, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
Let L be the set of all lines in XY-plane and R be the relation in L defined as R = {L1, L2) : L1 is parallel to L2}. Show that R is an equivalence relation. Find the set of all lines related to the line y= 2x + 4.
If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, 9} given by x R y ⇔ y = 3 x, then R = _____________ .
If A = {a, b, c, d}, then a relation R = {(a, b), (b, a), (a, a)} on A is _____________ .
Let R be the relation on the set A = {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Then, _____________________ .
The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is ___________________ .
In the set Z of all integers, which of the following relation R is not an equivalence relation ?
Mark the correct alternative in the following question:
The maximum number of equivalence relations on the set A = {1, 2, 3} is _______________ .
Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find (A × B) ∪ (A × C).
Write the relation in the Roster form and hence find its domain and range :
R1 = {(a, a2) / a is prime number less than 15}
Consider the set A = {1, 2, 3} and R be the smallest equivalence relation on A, then R = ______
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
symmetric but neither reflexive nor transitive
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, symmetric and transitive
Give an example of a map which is not one-one but onto
Give an example of a map which is neither one-one nor onto
Let A = {1, 2, 3} and consider the relation R = {1, 1), (2, 2), (3, 3), (1, 2), (2, 3), (1,3)}. Then R is ______.
Every relation which is symmetric and transitive is also reflexive.
Which of the following is not an equivalence relation on I, the set of integers: x, y
Let A = {1, 2, 3, 4, 5, 6} Which of the following partitions of A correspond to an equivalence relation on A?
If f(x) = `1 - 1/"x", "then f"("f"(1/"x"))` ____________.
Let R be the relation “is congruent to” on the set of all triangles in a plane is ____________.
Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is ____________.
Sherlin and Danju are playing Ludo at home during Covid-19. While rolling the dice, Sherlin’s sister Raji observed and noted the possible outcomes of the throw every time belongs to set {1,2,3,4,5,6}. Let A be the set of players while B be the set of all possible outcomes.
A = {S, D}, B = {1,2,3,4,5,6}
- Let R ∶ B → B be defined by R = {(x, y): y is divisible by x} is ____________.
An organization conducted a bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally, three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. Let B = {b1,b2,b3} G={g1,g2} where B represents the set of boys selected and G the set of girls who were selected for the final race.
Ravi decides to explore these sets for various types of relations and functions.
- Let R: B → B be defined by R = {(x, y): x and y are students of same sex}, Then this relation R is ____________.
Students of Grade 9, planned to plant saplings along straight lines, parallel to each other to one side of the playground ensuring that they had enough play area. Let us assume that they planted one of the rows of the saplings along the line y = x − 4. Let L be the set of all lines which are parallel on the ground and R be a relation on L.
Answer the following using the above information.
- Let relation R be defined by R = {(L1, L2): L1║L2 where L1, L2 ∈ L} then R is ____________ relation.
The relation > (greater than) on the set of real numbers is
Let R = {(a, b): a = a2} for all, a, b ∈ N, then R salifies.
Let f(x)= ax2 + bx + c be such that f(1) = 3, f(–2) = λ and f(3) = 4. If f(0) + f(1) + f(–2) + f(3) = 14, then λ is equal to ______.
Let A = {3, 5}. Then number of reflexive relations on A is ______.
Which relation is called an Empty Relation?
What should be checked to determine whether a relation is reflexive?
