Question:

Let $R$ be a relation defined on the set $\{1,2,3,4\}\times\{1,2,3,4\}$ by $R=\{((a,b),(c,d)):2a+3b=3c+4d\}$. Then the number of elements in $R$ is

Step-by-Step Solution

Key Concept: Need $2a+3b=3c+4d=k$. For each valid $k$, count pairs $(a,b)$ with $2a+3b=k$ and $(c,d)$ with $3c+4d=k$, multiply.

12 elements.

Correct Answer: 4