Is Person to Ancestor Relation a Function?
📺 Video Explanation
📝 Question
Consider the relation:
\[ \{(a,b): a \text{ is a person, } b \text{ is an ancestor of } a\} \]
Check:
- Is it a function?
- If yes, is it injective?
- Is it surjective?
✅ Solution
🔹 Is it a Function?
A relation is a function if every input has exactly one output.
Here:
- A person has many ancestors:
- parents
- grandparents
- great-grandparents
So one person can be related to many outputs.
❌ Therefore, it is not a function.
🎯 Final Answer
\[ \boxed{\text{This relation is not a function}} \]
So injective / surjective test does not apply.
🚀 Exam Shortcut
- Function needs exactly one image
- Ancestor relation gives many outputs
- So relation is not a function