Sets, Relations & Functions
Counting Elements in Relation via Linear Equation
nta_pyq_2023_apr
Grade 11
Question:
Let $A=\{1,2,3,4\}$ and $R=\{((a,b),(c,d)):\ 2a+3b=4c+5d\}$ on $A\times A$. Number of elements in $R$ is _________.
Step-by-Step Solution
Key Concept: Find pairs $((a,b),(c,d))$ with $a,b,c,d\in\{1,2,3,4\}$ satisfying $2a+3b=4c+5d$. Range of LHS: $[5,20]$, RHS: $[9,24]$. Overlap in $[9,20]$.
6 elements.
Correct Answer: 6