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
Correct option is
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)