GO Classes Test Series 2024 | Discrete Mathematics | Test 4 | Question: 21

Answer 1

Lets try to build the largest set in which no 2 numbers are divisible by one another

What i can do is add all primes to the list and exclude 1 because 1 divides every number(and of course it's not prime)

so I Get {3,5,7,11,13,17,19} NOW FROM remaining elements that are 1,9,15 and 21 . as soon as you add anything from these numbers to the set , 2numbers get divisible

 

hence least size required is 7+1=8

Comments

harshbbeer you missed 11 in {3,5,7,13,17,19}

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Edited, thx

Answer 2

Select all prime numbers , that is $7$ prime numbers. Then if you select one more number then we will get at least one pair of elements which divide each other. So, $8$ is the minimum possible answer. Hence, anything $\geq 8$ is answer.