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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

A
B
C
D
##### All statements are true
Solution

Correct option is

(B)

(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)

will have numbers {12 , 24 , 36,....} but these number will not come in ,

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)