Question

If \( A = \{1, 2, 3\} \), \( B = \{2, 3, 4\} \), then the function from A to B will be

• A. \( \{ (1, 2), (1, 3), (2, 3), (3, 3) \} \)
• B. \( \{ (1, 3), (2, 4) \} \)
• C. \( \{ (1, 3), (2, 2), (3, 3) \} \)
• D. \( \{ (1, 2), (2, 3), (3, 2), (3, 4) \} \)

Hint:

In a function, each element from the domain (set \( A \)) must be related to exactly one element from the codomain (set \( B \)).

Answer 1

The Correct Option is B

Step 1: Understanding a Function from \( A \) to \( B \):
A function from set \( A \) to set \( B \) is a set of ordered pairs where each element of \( A \) is related to exactly one element of \( B \). In other words, for each \( a \in A \), there should be a unique \( b \in B \) such that \( (a, b) \) is a pair in the function.

Step 2: Analyzing the Given Options:
Let's check each option to see which represents a valid function: \begin{itemize} \item (A) \( \{ (1, 2), (1, 3), (2, 3), (3, 3) \} \): This is not a function because \( 1 \) is related to both \( 2 \) and \( 3 \). A function cannot assign more than one value to an element in \( A \). \item (B) \( \{ (1, 3), (2, 4) \} \): This is a valid function because each element of \( A \) is related to exactly one element of \( B \). \item (C) \( \{ (1, 3), (2, 2), (3, 3) \} \): This is a valid function as well, but it doesn't match the format of the correct answer in the question. \item (D) \( \{ (1, 2), (2, 3), (3, 2), (3, 4) \} \): This is not a function because \( 3 \) is related to both \( 2 \) and \( 4 \), which violates the uniqueness condition of a function. \end{itemize}
Step 3: Conclusion:
The correct answer is option (B) \( \{ (1, 3), (2, 4) \} \), as it satisfies the condition for being a valid function.