हिंदी

Given A = {2, 3, 4}, B = {2, 5, 6, 7}. Construct an example of the following:an injective mapping from A to B

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

योग
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.

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Relations And Functions - Exercise [पृष्ठ १२]

APPEARS IN

एनसीईआरटी एक्झांप्लर Mathematics Exemplar [English] Class 12
अध्याय 1 Relations And Functions
Exercise | Q 18. (a) | पृष्ठ १२

संबंधित प्रश्न

Show that the relation R in the set A = {x ∈ Z : 0 ≤ x ≤ 12} given by R = {(a, b) : |a – b| is a multiple of 4} is an equivalence relation. Find the set of all elements related to 1.


Show that the relation R in the set A of points in a plane given by R = {(P, Q) : distance of the point P from the origin is the same as the distance of the point Q from the origin} is an equivalence relation. Further, show that the set of all points related to a point P ≠ (0, 0) is the circle passing through P with the origin as its centre.


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?


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 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}


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 father of y}


Test whether the following relation R1 is  (i) reflexive (ii) symmetric and (iii) transitive :

R1 on Q0 defined by (a, b) ∈ R1 ⇔ = 1/b.


Let A = {1, 2, 3}, and let R1 = {(1, 1), (1, 3), (3, 1), (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.


Give an example of a relation which is reflexive and transitive but not symmetric?


Show that the relation R on the set Z of integers, given by
R = {(a, b) : 2 divides a – b},  is an equivalence relation.


Let Z be the set of integers. Show that the relation
 R = {(a, b) : a, b ∈ Z and a + b is even}
is an equivalence relation on Z.


Show that the relation R, defined in the set A of all polygons as R = {(P1, P2) : P1 and P2 have the same number of sides}, is an equivalence relation. What is the set of all elements in A related to the right-angled triangle T with sides 3, 4 and 5?


If R and S are relations on a set A, then prove that R and S are symmetric ⇒ R ∩ S and R ∪ S are symmetric ?


Write the domain of the relation R defined on the set Z of integers as follows:-
(a, b) ∈ R ⇔ a2 + b2 = 25


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 ______________ .


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 `f(x) = (4x + 3)/(6x - 4), x ≠ 2/3`, show that fof (x) = x for all `x ≠ 2/3`. Also, find the inverse of f.


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 B × A.


Let A = {6, 8} and B = {1, 3, 5}.
Let R = {(a, b)/a∈ A, b∈ B, a – b is an even number}. Show that R is an empty relation from A to B.


In the set of natural numbers N, define a relation R as follows: ∀ n, m ∈ N, nRm if on division by 5 each of the integers n and m leaves the remainder less than 5, i.e. one of the numbers 0, 1, 2, 3 and 4. Show that R is equivalence relation. Also, obtain the pairwise disjoint subsets determined by R


Let Z be the set of integers and R be the relation defined in Z such that aRb if a – b is divisible by 3. Then R partitions the set Z into ______ pairwise disjoint subsets


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 neither one-one nor onto


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 ______.


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 ______.


Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : |a2 – b2| < 8. Then R is given by ______.


The relation R on the set A = {1, 2, 3} defined as R = {{1, 1), (1, 2), (2, 1), (3, 3)} is reflexive, symmetric and transitive.


Let A = { 2, 3, 6 } Which of the following relations on A are reflexive?


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 ____________.


The relation R is defined on the set of natural numbers as {(a, b) : a = 2b}. Then, R-1 is given by ____________.


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?

Find: `int (x + 1)/((x^2 + 1)x) dx`


On the set N of all natural numbers, define the relation R by a R b, if GCD of a and b is 2. Then, R is


A relation 'R' in a set 'A' is called reflexive, if


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 ______.


If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.


Which relation is an example of an Empty Relation for \(A=\{1,2\}\)?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×