Mathematics

Problem

Consider the sets

A=\{1,2,3\}

and

B=\{1,2,3\}

. A relation

R

is defined as the set of all ordered pairs

(a,b)\in A\times B

that satisfy the inequality

a<b

. a. (i) List explicitly all the ordered pairs belonging to

R

. b. (ii) Explain, without merely counting by inspection, why

|R|=3

. c. (iii) If instead

B=\{1,2,3,4\}

while

A

remains unchanged, describe a systematic procedure to determine

|R|

for the same condition

a<b

and state the final count obtained.