Let A = 1 , 2 , 3 , . ..20 . Let R 1 and R 2 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 __________.

Step-by-step solution

Given: A = 1 , 2 , 3 , . ..20 , R 1 = a , b : b is divisible by a and R 2 = a , b : a is an integral multiple of b . ⇒ 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 , 20 , 6 , 6 , 6 , 18 , . . . , 6 , 18 , 7 , 7 , 7 , 14 , 8 , 8 , 8 , 16 , 9 , 9 , 9 , 18 , 10 , 10 , 10 , 20 , 11 , 11 , . . . , 20 , 20 ⇒ n R 1 = 20 + 10 + 6 + 5 + 4 + 3 + 2 + 2 + 2 + 2 + 10 = 66 ⇒ R 1 ∩ R 2 = 1 , 1 , 2 , 2 , 3 , 3 ,