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Question: Answered & Verified by Expert

Let A=1,2,3,...20. Let R1 and R2 two relation on A such that

R1={a,b:b is divisible by a}

R2={a,b:a is an integral multiple of b}

Then, number of elements in R1R2 is equal to __________.

MathematicsSets and RelationsJEE MainJEE Main 2024 (01 Feb Shift 1)
Solution:
1315 Upvotes Verified Answer
The correct answer is: 46

Given: A=1,2,3,...20R1={a,b:b is divisible by a} and R2={a,b:a is an integral multiple of b}.

R1=1,1,1,2,...,1,20,2,2,2,4,...,2,20,3,3,3,6,...,3,18,4,4,4,8,...,4,20,5,5,5,10,...,5,20,6,6,6,18,...,6,18,7,7,7,14,8,8,8,16,9,9,9,18,10,10,10,20,11,11,...,20,20

nR1=20+10+6+5+4+3+2+2+2+2+10=66

R1R2=1,1,2,2,3,3,4,4,...,20,20

nR1R2=20

nR1-R2=nR1-nR1R2

nR1-R2=66-20

nR1-R2=46

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