The ordered pairs from A= {1, 2, 3, 4} are {(1, 1), (1, 2). (1, 3), (1, 4). (2, 1). (2, 2). (2, 3), (2, 4). (3, 1), (3, 2), (3, 3), (3, 4). (4. 1), (4, 2), (4, 3), (4, 4)}. As pka said there are 16 of those- 4 that start with 1, 4 that start with 2, 4 that start with 3. and 4 that star with 4.
The "relation" "3a+ 5b is a prime number" consists of all those pairs, (a. b), that satisfy. The only way to do this is to actually calculate 3a+ 5b for each pair.
(1,1): 3(1)+ 5(1)= 8. That is not a prime number so (1, 1) is not in the relation.
(1,2); 3(1)+ 5(2)= 13. That is a prime number so (1, 2) is in the relation.
(1,3): 3(1)+5(3)= 18. That is not a prime number so (1, 3) is not in the relation.
Can you complete this?