Subjects discrete math

Relation Analysis

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Relation Analysis


1. The problem involves understanding mappings between sets as shown in Graph B and Graph C, and analyzing the table A. 2. In Graph B, set x = \{1, -1\} and set y = \{-1, -2, -3, -4\}. The mappings are: - $1 \to -1$ and $1 \to -3$ - $-1 \to -2$ and $-1 \to -4$ 3. In Graph C, set x = \{-3, -2, -1, 0\} and set y = \{8, 7, 6, 5\}. The mappings are: - $-3 \to 8$ and $-3 \to 7$ - $-2 \to 6$ - $-1 \to 5$ - $0 \to 5$ 4. The table A shows pairs $(x,y)$: - $(5,1)$ - $(4,-2)$ - $(4,-3)$ - $(3,-4)$ 5. To analyze these, note that in Graph B and C, some elements in set x map to multiple elements in set y, indicating these are relations but not functions (since functions map each element of the domain to exactly one element in the codomain). 6. The table A also shows multiple y-values for the same x-value (e.g., $4 \to -2$ and $4 \to -3$), confirming it is a relation, not a function. 7. Summary: - Graph B and C represent relations with multiple outputs for some inputs. - Table A also represents a relation, not a function. No explicit function formula is given or requested.