Number of One-One and Onto Mappings
🎥 Video Explanation
📝 Question
Let set \(A\) have 5 elements and set \(B\) have 6 elements.
Find number of one-one and onto mappings from \(A\) to \(B\).
- A. 720
- B. 120
- C. 0
- D. none of these
✅ Solution
🔹 Step 1: Condition for Bijective Function
For a function to be one-one and onto (bijective):
Number of elements in domain = number of elements in codomain
—🔹 Step 2: Compare Sizes
\[ |A|=5,\quad |B|=6 \]
Since sizes are different:
❌ Cannot be onto ❌ Cannot be bijective
—🔹 Final Answer
\[ \boxed{\text{Option (C): 0}} \]