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Chapter 1: Problem 10

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

Short Answer

Expert verified
Out of the provided sets of ordered pairs, only sets (b) and (d) represent functions from set \(A\) to set \(B\).

Step by step solution

01

Set (a)

The set \(\{(a, 1),(c, 2),(c, 3),(b, 3)\}\) does not represent a function from \(A\) to \(B\) because the element 'c' from set \(A\) is associated with two different elements, 2 and 3, from set \(B\), which violates the definition of a function.
02

Set (b)

The set \(\{(a, 1),(b, 2),(c, 3)\}\) does represent a function from \(A\) to \(B\) because each element of set \(A\) is associated with exactly one element of set \(B\). 'a' is paired with 1, 'b' is paired with 2, and 'c' is paired with 3.
03

Set (c)

The set \(\{(1, a),(0, a),(2, c),(3, b)\}\) does not fit the criteria to be a function from \(A\) to \(B\) since the elements from \(B\) are associated with elements from \(A\), not vice versa. This set could potentially be a function from \(B\) to \(A\), but not from \(A\) to \(B\).
04

Set (d)

The set \(\{(c, 0),(b, 0),(a, 3)\}\) does represent a function from \(A\) to \(B\) because each element of set \(A\) is associated with exactly one element of set \(B\). Here, 'c' and 'b' are both paired with 0, and 'a' is paired with 3.

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