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Chapter 1: Problem 9

Which sets of ordered pairs represent functions from \(A\) to \(B ?\) Explain. \(A=\\{0,1,2,3\\}\) and \(B=\\{-2,-1,0,1,2\\}\) (a) \(\\{(0,1),(1,-2),(2,0),(3,2)\\}\) (b) \(\\{(0,-1),(2,2),(1,-2),(3,0),(1,1)\\}\) (c) \(\\{(0,0),(1,0),(2,0),(3,0)\\}\) (d) \(\\{(0,2),(3,0),(1,1)\\}\)

Short Answer

Expert verified
The set of ordered pairs (a) and (c) represent functions from \(A\) to \(B\). The sets (b) and (d) don't represent functions from \(A\) to \(B\) as they violate the definition of the function.

Step by step solution

01

Checking each set of ordered pairs

Analyze each set of ordered pairs to determine whether or not they meet the criteria for a function. The first elements of each pair should represent the set \(A\), and the second elements should represent the set \(B\). There should be no repetition in the first components of the ordered pairs.
02

Checking set (a)

\[(0,1),(1,-2),(2,0),(3,2)\] In this set, all elements in \(A\) are paired with exactly one element in \(B\). Every first component of the ordered pair is unique, which means this set does represent a function from \(A\) to \(B\).
03

Checking set (b)

\[(0,-1),(2,2),(1,-2),(3,0),(1,1)\] In this set, the element 1 in \(A\) is paired with two different elements in \(B\) (-2 and 1). Therefore, this set doesn't represent a function from \(A\) to \(B\).
04

Checking set (c)

\[(0,0),(1,0),(2,0),(3,0)\] In this set, all elements in \(A\) are paired with exactly one element in \(B\), which is 0 in this case. Hence, this set does represent a function from \(A\) to \(B\).
05

Checking set (d)

\[(0,2),(3,0),(1,1)\] In this set, the element 2 of \(A\) has not been paired with any element of \(B\). Therefore, this set doesn't represent a function from \(A\) to \(B\).

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