question 1 Enumerate the elements of the following relations

question 1. Enumerate the elements of the following relations from the set A of positive integers less than or equal to 10 to the set B of positive integers less than or equal to 30.

a. An element a of A is related to the element b of B if b = 3 × a

b. An element a of A is related to the element b of B if b = 2 × a - 1

Solution

A <= 10 and B <= 30

a) b = 3 xa. So, a is multiple of 3 and an element of b

So, a= 1 , 2,3----10

b = 1,2---30

So, b= 3, 6 , 9 , 12, 15 , 18 , 21, 24, 27 , 30 all mutiples of 3

but a =b/3 ---> 3, 6, 9 and <= 10

So, { 3, 6, 9 }

b) b = 2x a -1

a = 1,2 ---- 10

b = 2 -1 =1 ; b = 4-1 =3; b = 6-1 =5 ; b= 8-1 =7 ; b = 9 -1 =8

b= 10 -1 =9 ; b= 12 -1 =11; b= 14-1 =1 3

b = 16-1 =15 ; b= 18 -1 = 17 ; b= 20-1 = 19

So, solution { 1,3,5,7,8,9,11,12,15,17,19 }