Let A = { 1,2,3,...,20}. Let R_{1} and R_{2} be two

relation on A such that R_{1} = {(a,b):b is divisible by

a} R_{2} = {(a,b):a is an integral multiple of b} Then,

number of elements in R_{1} - R_{2} is equal to

Question

Let A = \ 1,2,3, ... ,20\. Let R_1 and R_2 be two relation on A such that R_1 = \(a,b):b is divisible by a\ R_2 = \(a,b):a is an integral multiple of b\ Then, number of elements in R_1 - R_2 is equal to

DivineJEE · Accepted Answer

(46) : R_1 = \(1,1),(1,2) ... (1,20),(2,2),(2,4), ... . (2,20),(3,3),(3,6) ... (3,18),(4,4),(4,8), ... .(4,20), (5,5),(5,10),(5,15),(5,20),(6,6),(6,12),(6,18),(7,7), (7,14),(8,8),(8,16),(9,9),(9,18),(10,10),(10,20), (11,11),(12,12),(13,13),(14,14),(15,15),(16,16), (17,17),(18,18),(19,19),(20,20)\ R_2 = \(20,1),(20,2),(20,4),(20,5),(20,10),(20,20), (19,19),(19,1),(18,1),(18,2),(18,3),(18,6),(18,9), (18,18),(17,1),(17,17),(16,1),(16,2),(16,4),(16,8), (16,16),(15,1),(15,3),(15,5),(15,15),(14,1),(14,2), (14,7),(14,14),(13,1),(13,13),(12,1),(12,2),(12,3), (12,4),(12,6),(12,12),(11,1),(11,11),(10,1),(10,2), (10,5),(10,10),(9,1),(9,3),(9,9),(8,1),(8,2),(8,4), (8,8),(7,1)(7,7),(6,1),(6,2),(6,3),(6,6),(5,1),(5,5), (4,1),(4,2),(4,4),(3,1),(3,3),(2,1),(2,2),(1,1)\ R_1 intersection R_2 = \(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7), (8,8),(9,9),(10,10),(11,11),(12,12),(13,13),(14,14), (15,15),(16,16),(17,17),(18,18),(19,19),(20,20)\ Number of elements in R_1 - R_2 = 66 - 20 = 46 elements. \

Explanation

The minimum number of elements that must be added to the relation R = {(a,b),(b,c),(b,d)} on the set { a,b,c,d} so that it is an equivalence relation is

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