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Which set of points does not represent a one-to-one function?

{(7,8),(5,5),(3,0),(4,8),(0,1)}

{(5,4),(7,1),(9,6),(6,8),(4,2)}

{(4,6),(0,2),(6,8),(2,5),(8,9)}

{(8,1),(9,9),(7,7),(1,3),(5,0)}

Which set of points does not represent a one-to-one function?\newline{(7,8),(5,5),(3,0),(4,8),(0,1)} \{(7,8),(5,5),(3,0),(4,8),(0,1)\} \newline{(5,4),(7,1),(9,6),(6,8),(4,2)} \{(5,4),(7,1),(9,6),(6,8),(4,2)\} \newline{(4,6),(0,2),(6,8),(2,5),(8,9)} \{(4,6),(0,2),(6,8),(2,5),(8,9)\} \newline{(8,1),(9,9),(7,7),(1,3),(5,0)} \{(8,1),(9,9),(7,7),(1,3),(5,0)\}

Full solution

Q. Which set of points does not represent a one-to-one function?\newline{(7,8),(5,5),(3,0),(4,8),(0,1)} \{(7,8),(5,5),(3,0),(4,8),(0,1)\} \newline{(5,4),(7,1),(9,6),(6,8),(4,2)} \{(5,4),(7,1),(9,6),(6,8),(4,2)\} \newline{(4,6),(0,2),(6,8),(2,5),(8,9)} \{(4,6),(0,2),(6,8),(2,5),(8,9)\} \newline{(8,1),(9,9),(7,7),(1,3),(5,0)} \{(8,1),(9,9),(7,7),(1,3),(5,0)\}
  1. Definition of One-to-One Function: A one-to-one function, also known as an injective function, is a function where each xx-value is paired with one unique yy-value, and no yy-value is repeated. To determine which set of points does not represent a one-to-one function, we need to check if any yy-value is repeated for different xx-values in each set.
  2. Check First Set of Points: Check the first set of points: (7,8),(5,5),(3,0),(4,8),(0,1){(7,8),(5,5),(3,0),(4,8),(0,1)}. We see that the yy-value 88 appears twice, once for x=7x=7 and once for x=4x=4. This means that this set of points does not represent a one-to-one function because the same yy-value is paired with more than one xx-value.
  3. Check Second Set of Points: Check the second set of points: (5,4),(7,1),(9,6),(6,8),(4,2){(5,4),(7,1),(9,6),(6,8),(4,2)}. All yy-values are unique for different xx-values. This set represents a one-to-one function.
  4. Check Third Set of Points: Check the third set of points: (4,6),(0,2),(6,8),(2,5),(8,9){(4,6),(0,2),(6,8),(2,5),(8,9)}. All yy-values are unique for different xx-values. This set represents a one-to-one function.
  5. Check Fourth Set of Points: Check the fourth set of points: (8,1),(9,9),(7,7),(1,3),(5,0){(8,1),(9,9),(7,7),(1,3),(5,0)}. All yy-values are unique for different xx-values. This set represents a one-to-one function.

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