Advertisements
Advertisements
Question
If A = {a, b, c}, B = (x , y} find B × B.
Solution
A = {a, b, c}, B = (x , y}
B × B = {(x, x), (x, y), (y, x), (y, y)}
APPEARS IN
RELATED QUESTIONS
determination of whether the following relations are reflexive, symmetric, and transitive:
Relation R in the set Z of all integers defined as
R = {(x, y): x − y is an integer}
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.
Let A be the set of all human beings in a town at a particular time. Determine whether of the following relation is reflexive, symmetric and transitive :
R = {(x, y) : x and y live in the same locality}
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.
Defines a relation on N :
x > y, x, y ∈ N
Determine the above relation is reflexive, symmetric and transitive.
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.
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-angled triangle T with sides 3, 4 and 5?
R is a relation on the set Z of integers and it is given by
(x, y) ∈ R ⇔ | x − y | ≤ 1. Then, R is ______________ .
Let A = {1, 2, 3}. Then, the number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is ______.
Let A = {1, 2, 3, 4}, B = {4, 5, 6}, C = {5, 6}. Find A × (B ∩ C).
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
reflexive, transitive but not symmetric
Give an example of a map which is not one-one but onto
If a relation R on the set {1, 2, 3} be defined by R = {(1, 2)}, then R is ______.
Given set A = {a, b, c}. An identity relation in set A is ____________.
Find: `int (x + 1)/((x^2 + 1)x) dx`
The relation > (greater than) on the set of real numbers is
A relation in a set 'A' is known as empty relation:-
lf A = {x ∈ z+ : x < 10 and x is a multiple of 3 or 4}, where z+ is the set of positive integers, then the total number of symmetric relations on A is ______.
If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.
