Question
Which relation is displayed in this table?
• {(3,3) , (3, 7) , (5,8) , (9,0)}
• {(3,3) , (3, 7), (5,9) , (8,0)}
• {(3,3), (7, 3), (5, 8), (9,0)}
• {(3,3), (7, 3), (8, 5), (0,9)}
• {(3,3) , (3, 7) , (5,8) , (9,0)}
• {(3,3) , (3, 7), (5,9) , (8,0)}
• {(3,3), (7, 3), (5, 8), (9,0)}
• {(3,3), (7, 3), (8, 5), (0,9)}
Answers
GPT-4o mini
To analyze the relations displayed in the tables you've provided, let's break each one down:
1. **Relation 1**: \(\{(3,3), (3, 7), (5, 8), (9, 0)\}\)
- Here, the first element (input) can be \(3\) and has two outputs \(3\) and \(7\).
- The element \(5\) maps to \(8\), and \(9\) maps to \(0\).
- This relation is **not a function** because \(3\) has two outputs.
2. **Relation 2**: \(\{(3,3), (3, 7), (5, 9), (8, 0)\}\)
- Similar to the first relation, the first element \(3\) has two outputs \(3\) and \(7\).
- The element \(5\) maps to \(9\), and \(8\) maps to \(0\).
- This relation is also **not a function** because \(3\) has two outputs.
3. **Relation 3**: \(\{(3,3), (7, 3), (5, 8), (9,0)\}\)
- Each input has a unique output: \(3\) maps to \(3\), \(7\) maps to \(3\), \(5\) maps to \(8\), and \(9\) maps to \(0\).
- This relation is also **not a function** as \(3\) and \(7\) both map to \(3\) (repeating output).
4. **Relation 4**: \(\{(3,3), (7, 3), (8, 5), (0,9)\}\)
- Here, the output of \(3\) is \(3\), \(7\) maps to \(3\), \(8\) maps to \(5\), and \(0\) maps to \(9\).
- This relation is also **not a function** because both \(3\) and \(7\) output to \(3\).
In conclusion, all provided relations are not functions as they do not satisfy the criteria of a function, where each input maps to exactly one output.
1. **Relation 1**: \(\{(3,3), (3, 7), (5, 8), (9, 0)\}\)
- Here, the first element (input) can be \(3\) and has two outputs \(3\) and \(7\).
- The element \(5\) maps to \(8\), and \(9\) maps to \(0\).
- This relation is **not a function** because \(3\) has two outputs.
2. **Relation 2**: \(\{(3,3), (3, 7), (5, 9), (8, 0)\}\)
- Similar to the first relation, the first element \(3\) has two outputs \(3\) and \(7\).
- The element \(5\) maps to \(9\), and \(8\) maps to \(0\).
- This relation is also **not a function** because \(3\) has two outputs.
3. **Relation 3**: \(\{(3,3), (7, 3), (5, 8), (9,0)\}\)
- Each input has a unique output: \(3\) maps to \(3\), \(7\) maps to \(3\), \(5\) maps to \(8\), and \(9\) maps to \(0\).
- This relation is also **not a function** as \(3\) and \(7\) both map to \(3\) (repeating output).
4. **Relation 4**: \(\{(3,3), (7, 3), (8, 5), (0,9)\}\)
- Here, the output of \(3\) is \(3\), \(7\) maps to \(3\), \(8\) maps to \(5\), and \(0\) maps to \(9\).
- This relation is also **not a function** because both \(3\) and \(7\) output to \(3\).
In conclusion, all provided relations are not functions as they do not satisfy the criteria of a function, where each input maps to exactly one output.