(i) Statement (i) is true because the intersection of the factors of 108 and 84 is equal to the factors of the highest common factor of 108 and 84, which is 12. (ii) Statement (ii) is not true because the multiples of 12 and 18 would not include numbers like 36. (iii) Statement (iii) is true because the intersection of the multiples of 12 and 18 is equal to the multiples of the least common multiple of 12 and 18, which is 36. (iv) Statement (iv) is true because the intersection of the multiples of 6 and 4 is identical to the multiples of 12, and the multiples of 12 are a subset of themselves.

1. Set Theory

2. Set Theory
Set Fn gives all factors of n. Set Mn gives all multiples of n less than 1000. Which of the
following statements is/are true?
(i) F108  F84 = F12
(ii) M12  M18 = M36
(iii) M12  M18 = M36
(iv) M12  (M6  M4)
(a) (i), (ii) and (iii) only
(b) (i), (iii) and (iv) only
(c) (i) and (iii) only
(d) All 4 statements

3. Set Theory
This is more a question on Number Systems than on Set Theory.
(a)F108  F84 = 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.
F108  F84 = F12. Statement A is true.
(b)M12 will have numbers {12, 24, 36, 48, ….} Numbers like 12, 24, … will not feature in
M36. So, Statement B cannot be true.

4. Set Theory
(c)M12  M18= Set of all numbers that are multiples of both 12 and 18. => this is set of
all common multiples of 12 and 18 => this is set of numbers that are multiples of the
least Common Multiple of 12 and 18.
LCM (12, 18) = 36. M12  M18= M36. Statement C is true.
(d) M6  M4 is identical to M12 {Explanation is exactly as we have seen in statement C}.
So, Statement D is also true. Bear in mind that M12 is a subset of itself. Statement D is
true.
Answer choice (b)

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