Check Whether Given Function is One-One and Onto

📺 Video Explanation

📝 Question

Given:

\[ A=\{2,3,4\},\quad B=\{a,b,c\} \]

and function:

\[ f=\{(2,a),(3,b),(4,c)\} \]

Check whether the function is one-one and onto.

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✅ Solution

🔹 Check One-One (Injective)

A function is one-one if different inputs have different outputs.

Here:

• \(2 \mapsto a\)
• \(3 \mapsto b\)
• \(4 \mapsto c\)

All outputs are distinct.

✔ Function is one-one.

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🔹 Check Onto (Surjective)

A function is onto if every element of codomain is used.

Codomain:

\[ B=\{a,b,c\} \]

Range:

\[ \{a,b,c\} \]

Since every element in \(B\) has pre-image:

✔ Function is onto.

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🎯 Final Answer

\[ \boxed{\text{The function is both one-one and onto}} \]

So, it is a bijective function.

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🚀 Exam Shortcut

• Unique outputs → one-one
• All codomain elements covered → onto
• Both true → bijection