To determine which of the given relations is NOT a function, we must examine each relation to see if it satisfies the definition of a function. Specifically, a function relates each input to exactly one output.
Relation 1: [tex]\(\{(0,1),(1,1),(2,1),(3,1)\}\)[/tex]
- Input 0 maps to 1.
- Input 1 maps to 1.
- Input 2 maps to 1.
- Input 3 maps to 1.
Each input has exactly one unique output, so this relation is a function.
Relation 2: [tex]\(\{(0,0),(3,4),(5,6),(8,9)\}\)[/tex]
- Input 0 maps to 0.
- Input 3 maps to 4.
- Input 5 maps to 6.
- Input 8 maps to 9.
Each input has exactly one unique output, so this relation is a function.
Relation 3: [tex]\(\{(0,0),(2,2),(4,4),(6,6)\}\)[/tex]
- Input 0 maps to 0.
- Input 2 maps to 2.
- Input 4 maps to 4.
- Input 6 maps to 6.
Each input has exactly one unique output, so this relation is a function.
Relation 4: [tex]\(\{(0,1),(0,2),(0,3),(0,4)\}\)[/tex]
- Input 0 maps to 1.
- Input 0 maps to 2.
- Input 0 maps to 3.
- Input 0 maps to 4.
Input 0 maps to multiple outputs (1, 2, 3, and 4), which means this relation does not satisfy the criteria for a function.
Therefore, the relation [tex]\(\{(0,1),(0,2),(0,3),(0,4)\}\)[/tex] is NOT a function.
The answer to the question is:
4. [tex]\(\{(0,1),(0,2),(0,3),(0,4)\}\)[/tex]
