1. **State the problem:** We are given a mapping from a set of inputs to outputs as follows: 2 maps to 8, 8 maps to 2, 5 maps to 5, and 7 has no output. 2. **Identify the type of relation:** This mapping can be viewed as a function or relation from the input set \{2,8,5,7\} to the output set \{8,2,5\}. 3. **Check if it is a function:** A function assigns exactly one output to each input. Here, each input except 7 has exactly one output, but 7 has no output, so this is a partial function or a relation but not a total function. 4. **Analyze the mapping:** - 2 \to 8 - 8 \to 2 - 5 \to 5 - 7 \to no output 5. **Determine if the function is one-to-one (injective):** - 2 maps to 8 - 8 maps to 2 - 5 maps to 5 No two inputs map to the same output, so it is injective. 6. **Determine if the function is onto (surjective):** - Outputs are 8, 2, 5 - Inputs 2, 8, 5 map to these outputs - 7 has no output, so the function is not defined for 7, but all outputs are covered by some input. 7. **Summary:** The relation is an injective partial function from inputs \{2,8,5,7\} to outputs \{8,2,5\} with 7 having no output. **Final answer:** The mapping is an injective partial function with domain \{2,8,5,7\} and codomain \{8,2,5\}, where 7 is not mapped to any output.