Question

Suppose that \( A = \{ 1, 2, 3 \} \), \( B = \{ 4, 5, 6, 7 \} \), and \( f = \{ (1, 4), (2, 5), (3, 6) \ \) be a function from \( A \) to \( B \). Then \( f \) is:}

• A. one-one
• B. onto
• C. not one-one
• D. none of these

Hint:

To check if a function is one-one, ensure that different inputs map to different outputs.

Answer 1

The Correct Option is A

Step 1: A function is one-one (injective) if for every distinct pair \( a, b \in A \), \( f(a) \neq f(b) \). In this case, \( f(1) = 4 \), \( f(2) = 5 \), and \( f(3) = 6 \), so each element in \( A \) maps to a distinct element in \( B \). Thus, the function is one-one.