Advertisements
Advertisements
प्रश्न
Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:
an injective mapping from A to B
Advertisements
उत्तर
Given, A = {2, 3, 4}, B = {2, 5, 6, 7}
Let f: A → B denote a mapping
f = {(x, y): y = x + 3}
or
f = {(2, 5), (3, 6), (4, 7)}, which is an injective mapping.
APPEARS IN
संबंधित प्रश्न
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}
Check whether the relation R in R defined by R = {(a, b) : a ≤ b3} is reflexive, symmetric or transitive.
Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.
Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y) : x and y have the same number of pages} is an equivalence relation.
Given an example of a relation. Which is reflexive and symmetric but not transitive.
Show that the relation R defined in the set A of all triangles as R = {(T1, T2) : T1 is similar to T2}, is an equivalence relation. Consider three right angle triangles T1 with sides 3, 4, 5, T2 with sides 5, 12, 13 and T3 with sides 6, 8, and 10. Which triangles among T1, T2 and T3 are related?
Show that the relation R defined in the set A of all polygons as R = {(P1, P2): P1 and P2 have same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right angle triangle T with sides 3, 4 and 5?
Let A = {1, 2, 3}. Then number of equivalence relations containing (1, 2) is ______.
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 is wife of y}
The following relation is defined on the set of real numbers.
aRb if 1 + ab > 0
Find whether relation is reflexive, symmetric or transitive.
Show that the relation R defined by R = {(a, b) : a – b is divisible by 3; a, b ∈ Z} is an equivalence relation.
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 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.
Define a symmetric relation ?
Define an equivalence relation ?
State the reason for the relation R on the set {1, 2, 3} given by R = {(1, 2), (2, 1)} to be transitive ?
A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : x R y ⇔ x is relatively prime to y. Then, domain of R 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, _____________________ .
S is a relation over the set R of all real numbers and it is given by (a, b) ∈ S ⇔ ab ≥ 0. Then, S is _______________ .
Mark the correct alternative in the following question:
The maximum number of equivalence relations on the set A = {1, 2, 3} is _______________ .
Show that the relation R on R defined as R = {(a, b): a ≤ b}, is reflexive, and transitive but not symmetric.
R = {(a, b) / b = a + 1, a ∈ Z, 0 < a < 5}. Find the Range of R.
Let L denote the set of all straight lines in a plane. Let a relation R be defined by lRm if and only if l is perpendicular to m ∀ l, m ∈ L. Then R is ______.
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:
symmetric but neither reflexive nor transitive
The following defines a relation on N:
x is greater than y, x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.
The following defines a relation on N:
x + y = 10, x, y ∈ N
Determine which of the above relations are reflexive, symmetric and transitive.
Let T be the set of all triangles in the Euclidean plane, and let a relation R on T be defined as aRb if a is congruent to b ∀ a, b ∈ T. Then R is ______.
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is ______.
A relation S in the set of real numbers is defined as `"xSy" => "x" - "y" + sqrt3` is an irrational number, then relation S is ____________.
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}
- The above-defined relation R 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 be a relation on B defined by R = {(1,2), (2,2), (1,3), (3,4), (3,1), (4,3), (5,5)}. Then R 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 ____________.
The relation > (greater than) on the set of real numbers is
Which one of the following relations on the set of real numbers R is an equivalence relation?
A relation 'R' in a set 'A' is called a universal relation, if each element of' A' is related to :-
Define the relation R in the set N × N as follows:
For (a, b), (c, d) ∈ N × N, (a, b) R (c, d) if ad = bc. Prove that R is an equivalence relation in N × N.
Given a non-empty set X, define the relation R in P(X) as follows:
For A, B ∈ P(X), (4, B) ∈ R iff A ⊂ B. Prove that R is reflexive, transitive and not symmetric.
