Question
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)
CAT 2021
Solution
Correct option is
(B)
Explanatory Answer
(i)
this is the set of all numbers that are factors of 108 and 84
hence we have to find common factors which , HIGHEST COMMON FACTOR OF 84 and 108
HCF (84,108)=12
hence this is true
(ii)
hence this statement is false
(iii)
∩
- This is the set of all common
multiples of 12 and 18 ,
so , LCM(12 , 18 ) = 36 , hence this statement is also true
(iv) LCM(6,4)= 12 , and every set is a subset of itself , Hence this is also true
so , correct option is B (i ,iii,iv)