Question

Let A-10, 1, 2, 3, 4, 5,6), let B = 10, 1, 2, 3, 4, 5,6, 7,8), and let R be the relation from A to B given by "the greatest common divisor of a and b is 2." [Note: "greatest common divisor" is sometimes called "highest common factor"] List the elements of R.

Answer 1

R = {(10,2), (10,4), (10,6), (10,8), (2,10), (2,2), (2,4), (2,6), (2,4), (4,10), (4,2), (4,6), (6,10), (6,2), (6,4), (6,8)}

Explanation:

A = (10, 1, 2, 3, 4, 5, 6)

B = (10, 1, 2, 3, 4, 5, 6, 7, 8)

R is a relation and defined as

R: A→B

R: The greatest common divisor of a and b is 2

To find the elements of R we need to find pair from A and B respectively.

R = {(10,2), (10,4), (10,6), (10,8), (2,10), (2,2), (2,4), (2,6), (2,4), (4,10), (4,2), (4,6), (6,10), (6,2), (6,4), (6,8)}

Now, these pairs were found by picking one element from A and checking with elements of B if they have a gcd of 2. If yes, they fall under the defined relation.