If A x x is a multiple of 7 B x x is a multiple of 5 and C x x is a multiple of 35 Then which one of...........

Quantitative Aptitude (CDS) Simplification

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If A = {x : x is a multiple of 7},

B = {x : x is a multiple of 5} and

C = {x : x is a multiple of 35},

Then which one of the following is a null set?

(A − B) U C

(A −B) − C

(A $\bigcap$ B) $\bigcap$ C

. (A $\bigcap$ B) − C

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Explanation:

According to question
A = {7,14,21,28,35,42 … … . . }
B = {5,10,15,20,25. … … . . }
C = {35,70,105 … … … }
Option (1):
(A − B) U C = {7,14,21,28,42 … . . } U {35,70,105 … … } ≠ ∅
Option (2):
(A − B) − C = {7,14,21,28,42 … . . } −{35,70,105 … … } ≠ ∅
Option (3):
(A $\bigcap$ B) $\bigcap$ C = {35,70 … . . }
Option (4):
(A ∩ B) − C = {35,70 … . } − {35,70 … } = ∅
Hence option (4)