Question

which relation is not a function? 1. diagram with 1→a, 2→b, 3→c 2. diagram with a→4, a→3, b→4, b→3, c→4, c→3 3. diagram with 2→8, 2→10, 2→12, 4→8, 4→10, 4→12, 6→8, 6→10, 6→12 4. diagram with 6→10, 6→12, 8→10, 8→12

Explanation:

Step1: Recall the definition of a function

A function is a relation where each input (element in the domain) has exactly one output (element in the codomain). In other words, no input value can be mapped to more than one output value.

Step2: Analyze each relation

• Relation 1: The domain elements are 1, 2, 3. Each domain element maps to exactly one codomain element (A, B, C respectively). So this is a function.
• Relation 2: The domain elements are A, B, C. Each domain element maps to exactly one codomain element (either 4 or 3, but each input has one output). So this is a function.
• Relation 3: The domain elements are 2, 4, 6. Each domain element maps to exactly one codomain element (8, 10, or 12, but each input has one output). So this is a function.
• Relation 4: The domain elements are 6 and 8. The element 6 maps to both 10 and 12, and the element 8 also maps to both 10 and 12. So each input (6 and 8) has more than one output, which violates the definition of a function.

Answer:

4 (the fourth relation, where 6 maps to 10 and 12, and 8 maps to 10 and 12)