Advertisements
Advertisements
Question
Give an example of a map which is one-one but not onto
Advertisements
Solution
Let f: N → N, be a mapping defined by f(x) = x2
For f(x1) = f (x2)
Then, `x_1^2 = x_2^2`
x1 = x2 ......(Since x1 + x2 = 0 is not possible)
Further ‘f’ is not onto, as for 1 ∈ N, there does not exist any x in N such that f(x) = 2x + 1.
APPEARS IN
RELATED QUESTIONS
Show that the relation R in the set R of real numbers, defined as R = {(a, b) : a ≤ b2} is neither reflexive nor symmetric nor transitive.
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, transitive but not symmetric ?
If A = {1, 2, 3, 4} define relations on A which have properties of being reflexive, symmetric and transitive ?
Show that the relation '≥' on the set R of all real numbers is reflexive and transitive but not symmetric ?
Give an example of a relation which is transitive but neither reflexive nor symmetric?
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.
Let n be a fixed positive integer. Define a relation R on Z as follows:
(a, b) ∈ R ⇔ a − b is divisible by n.
Show that R is an equivalence relation on Z.
Let S be a relation on the set R of all real numbers defined by
S = {(a, b) ∈ R × R : a2 + b2 = 1}
Prove that S is not an equivalence relation on R.
If A = {2, 3, 4}, B = {1, 3, 7} and R = {(x, y) : x ∈ A, y ∈ B and x < y} is a relation from A to B, then write R−1.
Let A = {2, 3, 4, 5} and B = {1, 3, 4}. If R is the relation from A to B given by a R b if "a is a divisor of b". Write R as a set of ordered pairs.
Let R be the equivalence relation on the set Z of the integers given by R = { (a, b) : 2 divides a - b }.
Write the equivalence class [0].
Let A = {0, 1, 2, 3} and R be a relation on A defined as
R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}
Is R reflexive? symmetric? transitive?
Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : | a2- b2 | < 8}. Write R as a set of ordered pairs.
R is a relation on the set Z of integers and it is given by
(x, y) ∈ R ⇔ | x − y | ≤ 1. Then, R is ______________ .
The relation R = {(1, 1), (2, 2), (3, 3)} on the set {1, 2, 3} is ___________________ .
Mark the correct alternative in the following question:
Let R be a relation on the set N of natural numbers defined by nRm if n divides m. Then, R is _____________ .
Show that the relation R on the set Z of integers, given by R = {(a,b):2divides (a - b)} is an equivalence relation.
For the matrix A = `[(2,3),(5,7)]`, find (A + A') and verify that it is a symmetric matrix.
If A = {a, b, c}, B = (x , y} find A × A.
Write the relation in the Roster form and hence find its domain and range:
R2 = `{("a", 1/"a") "/" 0 < "a" ≤ 5, "a" ∈ "N"}`
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
Give an example of a map which is not one-one but onto
The following defines a relation on N:
x y is square of an integer x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.
Consider the non-empty set consisting of children in a family and a relation R defined as aRb if a is brother of b. Then R is ______.
An integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.
Let A = {1, 2, 3} and R = {(1, 2), (2, 3), (1, 3)} be a relation on A. Then, R is ____________.
Let A = {1, 2, 3}, then the domain of the relation R = {(1, 1), (2, 3), (2, 1)} defined on A is ____________.
If f(x) = `1 - 1/"x", "then f"("f"(1/"x"))` ____________.
Let A = {x : -1 ≤ x ≤ 1} and f : A → A is a function defined by f(x) = x |x| then f is ____________.
A relation R in set A = {1, 2, 3} is defined as R = {(1, 1), (1, 2), (2, 2), (3, 3)}. Which of the following ordered pair in R shall be removed to make it an equivalence relation in A?
Given triangles with sides T1: 3, 4, 5; T2: 5, 12, 13; T3: 6, 8, 10; T4: 4, 7, 9 and a relation R inset of triangles defined as R = `{(Delta_1, Delta_2) : Delta_1 "is similar to" Delta_2}`. Which triangles belong to the same equivalence class?
A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible to vote and voter turnout was about 67%, the highest ever
Let I be the set of all citizens of India who were eligible to exercise their voting right in the general election held in 2019. A relation ‘R’ is defined on I as follows:
R = {(V1, V2) ∶ V1, V2 ∈ I and both use their voting right in the general election - 2019}
- Mr. Shyam exercised his voting right in General Election-2019, then Mr. Shyam is related to which of the following?
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 = {(1,1),(1,2), (2,2), (3,3), (4,4), (5,5), (6,6)}, then R is ____________.
If A is a finite set consisting of n elements, then the number of reflexive relations on A is
A relation 'R' in a set 'A' is called a universal relation, if each element of' A' is related to :-
A relation 'R' in a set 'A' is called reflexive, if
Let a set A = A1 ∪ A2 ∪ ... ∪ Ak, where Ai ∩ Aj = Φ for i ≠ j, 1 ≤ i, j ≤ k. Define the relation R from A to A by R = {(x, y): y ∈ Ai if and only if x ∈ Ai, 1 ≤ i ≤ k}. Then, R is ______.
Let A = {3, 5}. Then number of reflexive relations on A is ______.
