Assertion (A) : The function
`f:(1,2,3)to(a,b,c,d)` defined by
`f={(1,a),(2,b),(3,c)}` has no inverse.
Reason (R) f is not one-one.

Options

A. Both A and R are individually true, and R is the correct explanation of A
B. Both A and R are individually true but R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true

Explanation

To solve the given problem, we need to analyze the assertion and the reason provided.

### Step 1: Understand the Assertion
The assertion states that the function \( f: \{1, 2, 3\} \to \{a, b, c, d\} \) defined by \( f = \{(1, a), (2, b), (3, c)\} \) has no inverse.

### Step 2: Analyze the Function
The function \( f \) maps the elements from the set \( \{1, 2, 3\} \) to the elements \( \{a, b, c, d\} \). Specifically, it maps:
- \( 1 \) to \( a \)
- \( 2 \) to \( b \)
- \( 3 \) to \( c \)

### Step 3: Check if the Function is One-One
A function is one-one (injective) if different inputs map to different outputs. In this case:
- \( 1 \) maps to \( a \)
- \( 2 \) maps to \( b \)
- \( 3 \) maps to \( c \)

Since all outputs \( a, b, c \) are distinct, the function is indeed one-one.

### Step 4: Determine the Inverse
For a function to have an inverse, it must be both one-one and onto (surjective). The function \( f \) is one-one, but it does not map to \( d \) in the codomain \( \{a, b, c, d\} \). Therefore, it is not onto.

### Step 5: Conclusion on the Assertion
Since the function is not onto, it cannot have an inverse. Thus, the assertion that the function has no inverse is true.

### Step 6: Analyze the Reason
The reason states that \( f \) is not one-one. However, we have established that \( f \) is indeed one-one. Therefore, the reason is false.

### Final Conclusion
- The assertion is true: The function has no inverse.
- The reason is false: The function is one-one.

Thus, the correct answer is that the assertion is true, but the reason is false.

### Summary of the Solution
- Assertion (A) is true: The function has no inverse.
- Reason (R) is false: The function is one-one.