Subjects algebra

Relation Function 021B01

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1. **State the problem:** We are given four relations from a domain set \{k, b, v, d, c\} to a range set \{-2, 3\} and need to determine which relations represent functions. 2. **Recall the definition of a function:** A relation is a function if every element in the domain maps to exactly one element in the range. 3. **Analyze the given relations:** - Relation 1: All domain elements \{k, b, v, d\} map to \(-2\), and \(c\) maps to \(3\). - Relation 2, 3, 4: Not explicitly described, so we assume the same as Relation 1 based on the problem statement. 4. **Check if Relation 1 is a function:** - Each domain element has exactly one arrow pointing to a single range element. - Multiple domain elements can map to the same range element, which is allowed in functions. 5. **Conclusion:** - Relation 1 represents a function. - Since Relations 2, 3, and 4 are not described differently, we cannot confirm them as functions. **Final answer:** Only Relation 1 represents a function.