Relations

In the realm of mathematics, Relations serve as the bridges that connect elements from diverse sets. These connections can be depicted through various methods including sets of ordered pairs, matrices, or even graphical illustrations. Specific types of relations, such as equivalence and ordering relations, exhibit unique properties that are widely applied across multiple mathematical disciplines.

Determining if the Relation is a Function

Question Which set of ordered pairs does not represent a function? Answer $\{(5,-8),(3,5),(3,-3),(2,8)\}$ $\{(-6,-6),(8,2),(1,-6),(-2,-2)\}$ $\{(-1,-3),(0,2),(4,-6),(-2,2)\}$ $\{(5,-4),(-7,-1),(-8,7),(-5,4)\}$
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Finding the Domain and Range of the Relation

Find the domain and range of the relation \( R = \{ (x, y) | y = 2x + 3 \} \).
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Finding the Inverse

Find the inverse of the function \( f(x) = 3x - 7 \).
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Determining if One Relation is the Inverse of Another

Given two relations \(R = \{(2, 3), (4, 5), (6, 7)\}\) and \(S = \{(3, 2), (5, 4), (7, 6)\}\), determine if relation \(S\) is the inverse of relation \(R\).
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Determining if Surjective (Onto)

Is the function \( f: \mathbb{R} \rightarrow \mathbb{R}, f(x) = x^3 \) surjective?
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Determining if Bijective (One-to-One)

Let the function f: A->B be defined as f(x) = 2x + 3, where A and B are sets of integers. Determine if the function is bijective (one-to-one and onto).
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Popular Problems

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