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Relation of Sets
A relation R consists of the followings:
(i) Two sets say A and B (ii) an open sentence P(x, y) in which P(a, b) is either true or false for any ordered pair (a, b)
A × B, then R is called a relation from A to B and is denoted by
R = {A, B, P(x, y)}.
It may be noted that, here R does not stand for the set of real numbers.
Relation R in a set
If the set B = A, then the relation R is said to be defined in the set A or R is a relation in the set A and
R = {A, A, P(x, y)}.
Further, if P(a, b) is true we say that “a is related to b in the sense of R” and is written as aRb.
In case, P(a, b) is not true we say that a is not related to b in the sense of R and is written as a R b.
Illustration 1: let A = {1, 2, 3} ; B = {1, 6} and P (x, y) = x is less than y, then A × B = {(1, 1), (1, 6), (2, 1), (2, 6), (3, 1), (3, 6)}.
We notice that the following ordered pairs have the property x < y,
(1, 6), (2, 6) and (3, 6).
Hence R = {(1, 6), (2, 6), (3, 6)}.
We also notice that R is a subset of A × B.
Definition of relation: A relation R from a set A to the set B is a subset of A × B i.e. R ⊆ A × B.
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(i) Two sets say A and B (ii) an open sentence P(x, y) in which P(a, b) is either true or false for any ordered pair (a, b)
R = {A, B, P(x, y)}.
It may be noted that, here R does not stand for the set of real numbers.
Relation R in a set
If the set B = A, then the relation R is said to be defined in the set A or R is a relation in the set A and
R = {A, A, P(x, y)}.
Further, if P(a, b) is true we say that “a is related to b in the sense of R” and is written as aRb.
In case, P(a, b) is not true we say that a is not related to b in the sense of R and is written as a R b.
Illustration 1: let A = {1, 2, 3} ; B = {1, 6} and P (x, y) = x is less than y, then A × B = {(1, 1), (1, 6), (2, 1), (2, 6), (3, 1), (3, 6)}.
We notice that the following ordered pairs have the property x < y,
(1, 6), (2, 6) and (3, 6).
Hence R = {(1, 6), (2, 6), (3, 6)}.
We also notice that R is a subset of A × B.
Definition of relation: A relation R from a set A to the set B is a subset of A × B i.e. R ⊆ A × B.
Services: - Relation of Sets Homework | Relation of Sets Homework Help | Relation of Sets Homework Help Services | Live Relation of Sets Homework Help | Relation of Sets Homework Tutors | Online Relation of Sets Homework Help | Relation of Sets Tutors | Online Relation of Sets Tutors | Relation of Sets Homework Services | Relation of Sets
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