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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