Consider the following statements in respect of a relation \(R\) from a set \(A\) to a set \(B\):
I. The set \(B\) is called codomain of the relation \(R\).
II. The range of the relation is always equal to codomain of the relation \(R\).
III. The domain of the relation \(R\) must be equal to the set \(A\).
Which of the statements given above is/are correct?
I only
Statement I is correct since set \(B\) is, by definition, the codomain of the relation \(R\) from \(A\) to \(B\). Statement II is incorrect because the range (the set of second elements actually occurring) is only a subset of the codomain, not necessarily equal to it. Statement III is also incorrect because the domain of \(R\) is the set of first elements of its ordered pairs, which is a subset of \(A\) and need not equal \(A\) entirely. Hence only statement I is correct.
Similar Questions
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Important Questions from Types of Relations
A Relation in R is defined as R = {(a, b) : a ≤ b2} is ________.
Let S = {1, 2, 3, ...}, A relation R on S × S is defined by xRy if log ax > log ay when a \(\rm = \frac 1 2.\) Then the relation is:
- Let A be {I, m, n}. Let the relation R be {}. Which of the following statements about R is true?
- Which of the following relations is symmetric but neither reflexive nor transitive for a set A= {a, b, c}?
Consider the following relations on the set {1, 2, 3, 4}:
R1 = {(1, 1),(1, 2), (1, 4),(2, 1), (2, 2), (3, 3),(4, 1), (4, 4)}
R2 = {(2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}
R3 = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (2, 3 ), (2, 4), (3, 3), (3, 4), (4, 4)}
R4 = {(1, 1), (1, 2), (2, 1), (2, 2), (3, 4), (4, 1), (4, 4)}
Which of these relations are reflexive and transitive but NOT symmetric?
