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Relations
Counting Relations
Premium Question
Grade 11

Question:

The total number of relations from a set $A$ with $m$ elements to a set $B$ with $n$ elements is:
(1) $2^{mn}$
(2) $2^{m+n}$
(3) $mn$
(4) $2^m \cdot 2^n$

Step-by-Step Solution

Key Concept: A relation from $A$ to $B$ is any subset of $A \times B$. Since $|A \times B| = mn$, the number of subsets is $2^{mn}$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)

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