The question is from CAT Set theory. It is about factors and multiples of some numbers and their union and intersection. CAT exam is known to test on basics rather than high funda ideas. CAT also tests multiple ideas in the same question, and 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. Set Theory (especially constructing venn diagrams) is a frequently tested topic. Make sure you know the basics from this chapter.

Question 1: Set F_{n} gives all factors of n. Set M_{n} gives all multiples of n less than 1000. Which of the following statements is/are true?

i. F_{108} ∩ F_{84} = F_{12}

ii. M_{12} ∪ M_{18} = M_{36}

iii. M_{12} ∩ M_{18} = M_{36}

iv. M_{12} ⊂ (M_{6} ∩ M_{4})

- i, ii and iii only
- i, iii and iv only
- i and iii only
- All statements are true

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i. F_{108} ∩ F_{84}

This is the set of all numbers that are factors of both 108 and 84

=> this is set of all common factors of 84 and 108

=> this is set of numbers that are factors of the Highest Common Factor of 84 and 108.

HCF (84, 108) = 12.

F_{108} ∩ F_{84} = F_{12} - this is true.

ii. M_{12} will have numbers {12, 24, 36, 48, ….} Numbers like 12, 24, … will not feature in M_{36}.

So, Statement B cannot be true.

iii. M_{12} ∩ M_{18} - this is the set of all common multiples of 12 and 18.

This is the set of numbers that are multiples of the Least Common Multiple of 12 and 18. (which is 36).

This statement is also true.

iv. Using the same logic as that used in statement iii, we can determine that statement iv is also true. Remember that every set is a subset of itself.

The question is **"Which of the following statements is/are true?"**

Choice B is the correct answer.

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