Let A = {3, 5, 7} and B = {15, 16, 17, 18}, and define a relation R from A to B as follows: For all (x, y) ? A × B,

Question

(x, y) ? R ? y/x is an integer.

(a) Is 3 R 15? Is 3 R 16? Is (7, 17) ? R? Is (3, 18) ? R?
(b) Write R as a set of ordered pairs.
(c) Write the domain and co-domain of R.
(d) Draw an arrow diagram for R.
(e) Is R a function from A to B? Explain.

Answer 1

a. Yes; No; No; Yes
b. {(3; 15); (3; 18); (5; 15)}
c. domain is {3; 5; 7}; co-domain is {15; 16; 17; 18}.
d. Draw an arrow diagram for R.
e. No: R fails both conditions for being a function from A to B. (1) Elements 5 and 7 in A are not
related to any elements in B, and (2) there is an element in A, namely 3, that is related to two different
elements in B, namely 15 and 18.