Question

Let W = (a, b, c, d). Determine whether each set of ordered pairs is a function from W into W. (a) ((b, a), (c, d), (d, a), (c, d), (a, d)) (c) ((a, b). (b, b). (e, b), (d, b)] (b) ((d, d), (c, a), (a, b), (d, b)]

(d) ((a, a), (b, a), (a, b), (c,d))​

Answer 1

Option b is correct.

• A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
• The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs. A mapping from A to B will only be a function if every element in set A has one end and only one image in set B. Let A & B be any two non-empty sets.

Here, according to the given information, we are given that, W = (a, b, c, d).

Then, we have,

A function is a relationship or collection of ordered pairs where each x-coordinate has a specific value assigned to it as the y-coordinate.

Only relation $R_{2}$ satisfies this criteria. The value of an is not unique in $R_{1}$ and $R_{4}$, while the value of b is not unique in $R_{3}$.

Thus, choice B is the appropriate response.

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