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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
i, ii and iii only
CORRECT ANSWER WRONG ANSWER
B
i, iii and iv only
CORRECT ANSWER WRONG ANSWER
C
i and iii only
CORRECT ANSWER WRONG ANSWER
D
All statements are true
CORRECT ANSWER WRONG ANSWER
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)

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)