Question

Consider the set T = {1, 2, 3, 4, 5, 6}. Let R = {(a, b) | a divides b} be a relation on the set T. Identify the missing ordered pairs from the given list. The list of all ordered pairs in the given relation R on the set T is (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), _____, (4, 4), (5, 5), and (6, 6).

Answer 1

Answer:  The missing ordered pairs are  (2, 2), (2, 4), (2, 6), (3, 3) and (3, 6).

Step-by-step explanation:  We are given the following set :

T = {1, 2, 3, 4, 5, 6}.

And, R = {(a, b) | a divides b} be a relation on the set T.

We are to identify the missing pairs from the following list of all ordered pairs in the given relation R on the set T :

{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), _____, (4, 4), (5, 5), and (6, 6).}.

Since R contains the ordered pairs (a, b) such that a divides b, so all the ordered pairs in R are

(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (5, 5), and (6, 6).

Thus, the missing ordered pairs are  (2, 2), (2, 4), (2, 6), (3, 3) and (3, 6).