Question:
If $A=\{1,2,3,4\}$. A relation from set $A$ to $A$ is defined as $(a,b)\,R\,(c,d)$ such that $2a+3b=3c+4d$. Find the number of elements in the relation.
If $A=\{1,2,3,4\}$. A relation from set $A$ to $A$ is defined as $(a,b)\,R\,(c,d)$ such that $2a+3b=3c+4d$. Find the number of elements in the relation.
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When relations involve algebraic expressions, systematically evaluate all ordered pairs from the given finite sets.
Updated On: Jan 24, 2026
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The Correct Option is C
Solution and Explanation
Step 1: List all possible ordered pairs from set $A$.
Since $A=\{1,2,3,4\}$, the total number of ordered pairs $(a,b)$ is: \[ 4\times 4=16 \] Step 2: Evaluate the expression $2a+3b$ for all pairs.
Compute the values of $2a+3b$ for all $(a,b)\in A\times A$.
Step 3: Find matching pairs $(c,d)$.
For each value obtained from $2a+3b$, count the number of ordered pairs $(c,d)$ such that: \[ 3c+4d=2a+3b \] Step 4: Count all valid relations.
On evaluating all possible combinations, the total number of elements satisfying the relation is: \[ 11 \]
Since $A=\{1,2,3,4\}$, the total number of ordered pairs $(a,b)$ is: \[ 4\times 4=16 \] Step 2: Evaluate the expression $2a+3b$ for all pairs.
Compute the values of $2a+3b$ for all $(a,b)\in A\times A$.
Step 3: Find matching pairs $(c,d)$.
For each value obtained from $2a+3b$, count the number of ordered pairs $(c,d)$ such that: \[ 3c+4d=2a+3b \] Step 4: Count all valid relations.
On evaluating all possible combinations, the total number of elements satisfying the relation is: \[ 11 \]
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