Question

Select the relations that are functions.

A. {(a, 1), (6, 1), (C, 1)}

B. {(a, a), (a, b), (a, c)}

C. {(1, a), (2, b), (3, a)}

D. {(a, a), (a, b), (a, c)}

Answer 1

Options A and C are functions because each input maps to exactly one output, whereas options B and D have the same input with different outputs, which disqualifies them as functions.

Step-by-step explanation:

The question asks to select the relations that qualify as functions. Recall that in a function, every input (usually represented by the first component of an ordered pair) must map to exactly one output (the second component). If an input has multiple outputs, it is not a function.

• Option A: {(a, 1), (6, 1), (C, 1)} can be a function since all different inputs have one output.
• Option B: {(a, a), (a, b), (a, c)} is not a function because the same input 'a' maps to multiple outputs 'a', 'b', and 'c'.
• Option C: {(1, a), (2, b), (3, a)} is a function because each input has a unique output.
• Option D: {(a, a), (a, b), (a, c)} is not a function for the same reason as option B.

Therefore, options A and C are functions.