No collaboration is permitted on the quizzes. Calculators are not permitted. Please ring your section below:

Question:
Version A: Let R be the relation on A = {1, 2,…, 10} with R = {(a,b) : a > b}.
Version B: Let R be the relation on A = {1, 2,…, 10} with R = {(a,b) : a = b + 1}
Version C: Let R be the relation on A = {1, 2,…, 10} with R = {(a,b) : a≠b}.

1. How many nonzero entries are there in the matrix representing R? (You can express your answer as an integer or a product of integers.)
2. Is R transitive? (Justify your answer.)