Determining if the Relation is a Function
Given the relation \( R = \{(1, 3), (2, 3), (1, 4), (2, 5)\} \), determine if the relation is a function.
Finding the Domain and Range of the Relation
Find the domain and range of the relation \( R = \{ (1,2), (3,4), (5,6), (7,8) \} \).
Finding the Inverse of the Relation
Let the relation \( R \) be defined on the set of real numbers by \( R = \{(x, y) | x = 2y + 3\} \). Find the inverse of the relation \( R \).
Determining if Surjective (Onto)
Let's consider a function \(f: A \rightarrow B\) where \(A = \{1, 2, 3, 4\}\) and \(B = \{5, 6, 7, 8\}\). The function is defined as \(f(x) = x + 4\). Is this function surjective (onto)?
Determining if Bijective (One-to-One)
Given the relation \( R = \{(1, 2), (2, 3), (3, 4), (4, 5)\} \), determine if it is bijective.