Let A be the set of all human beings in a town at a particular time. Determine whether each of the following relations are reflexive, symmetric and transitive: R = {(x, y) : x and y work at the same place} Watch Solution
Let A be the set of all human beings in a town at a particular time. Determine whether each of the following relations are reflexive, symmetric and transitive: R = {(x, y) : x is wife of y} Watch Solution
Let A be the set of all human beings in a town at a particular time. Determine whether each of the following relations are reflexive, symmetric and transitive: R = {(x, y) : x is father of y} Watch Solution
Relations R1, R2, R3 and R4 are defined on a set A = {a, b, c} as follows : R1 = {(a, a) (a, b) (a, c) (b, b) (b, c), (c, a) (c, b) (c, c)} R2 = {(a, a)} R3 = {(b, a)} R4 = {(a, b) (b, c) (c, a)} Find whether or not each of the relations R1, R2, R3, R4 on A is (i) reflexive (ii) symmetric (iii) transitive Watch Solution
Test whether the relation R1 is (i) reflexive (ii) symmetric and (iii) transitive : R1 on Q0 defined by (a, b) ∈ R1⇔ a = 1/b Watch Solution
Test whether the relation R2 is (i) reflexive (ii) symmetric and (iii) transitive : R2 on Z defined by (a, b) ϵ R2⇔ |a – b| ≤ 5 Watch Solution
Test whether the relation R3 is (i) reflexive (ii) symmetric and (iii) transitive : R3 on R defined by (a, b) ∈ R3⇔ a^2 – 4 ab + 3b^2= 0. Watch Solution
Let A = {1, 2, 3}, and let R1 = {(1, 1), (1, 3), (3, 1), (2, 2), (2, 1), (3, 3), (2, 2), (2, 1), (3, 3)}, R2={(2,2),(3,1), (1, 3)}, R3 = {(1, 3),(3, 3)}. Find whether or not each of the relations R1, R2, R3 on A is (i) reflexive (ii) symmetric (iii) transitive Watch Solution
The following relations are defined on the set of real numbers : aRb if a – b greater than 0 ,(ii) aRb if 1 + ab greater than 0 ,(iii) aRb if | a | ≤ b Find whether these relations are reflexive, symmetric or transitive. Watch Solution
Check whether the relation R defined on the set A={1,2,3,4,5,6} as R= {(a, b) : b = a + 1} is reflexive, symmetric or transitive. Watch Solution
Check whether the relation R on R defined by R = {(a, b) : a ≤ b^3} is reflexive, symmetric or transitive. Watch Solution
Prove that every identity relation on a set is reflexive, but the converse is not necessarily true. Watch Solution
If A = {1, 2, 3, 4}, define relations on A which have properties of being (i) reflexive, transitive but not symmetric. (ii) symmetric but neither reflexive nor transitive (iii) reflexive, symmetric and transitive Watch Solution
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 Watch Solution
Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons. Watch Solution
An integer m is said to be related to another integer n if m is a multiple of n. Check if the relation is symmetric, reflexive and transitive. Watch Solution
Show that the relation “≥” on the set R of all real numbers is reflexive and transitive but not symmetric. Watch Solution
Give an example of a relation which is (i) reflexive and symmetric but not transitive (ii) reflexive and transitive but not symmetric (iii) symmetric and transitive but not reflexive (iv) symmetric but neither reflexive nor transitive (v) transitive but neither reflexive nor symmetric Watch Solution
Given the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3}, add a minimum number ordered pairs so that the enlarged relation is symmetric, transitive and reflexive. Watch Solution
Let A = {1, 2, 3} and R = {(1, 2), (1, 1), (2, 3)} be a relation on A. What minimum number of ordered pairs may be added to R so that it may become a transitive relation on A. Watch Solution
Let A = {a, b, c} and the relation R be defined on A as follows R={(a,a), (b, c), (a, b)}. Then, write a minimum number of ordered pairs to be added in R to make it reflexive and transitive Watch Solution
Relation on N : x greater than y, x, y ∈ N Determine the above relations are reflexive, symmetric and transitive. Watch Solution
Relation on N : x + y = 10, x, y ∈ N Determine the above relations are reflexive, symmetric and transitive. Watch Solution
Relation on N : xy is square of an integer, x, y ∈ N Determine the above relations are reflexive, symmetric and transitive. Watch Solution
Relation on N : x + 4y = 10, x, y ∈ N Determine the above relations are reflexive, symmetric and transitive. Watch Solution
