1. Which of the following ordered pairs belongs to the binary

relation p on N?

a) x p y if & only if x + y < 7; (1,3), (2,5), (3,3), (4,4)

c) x p y if & only if 2x + 3y = 10; (5,0), (2,2), (3,1), (1,3)

2. S = {0, 1, 2, 4, 6}. Which of the following relations are

reflexive, symmetric, anti symmetric, and transitive? Find the

closures for each category for all of them

1.p = { (0,0), (1,1) (2,2) (4,4) (6,6) (0,1) (1,2) (2,4) (4,6)}

2. p = {(0,0), (1,1) (2,2) (4,4) (6,6) (4,6) (6,4)}

3. p = {(0,1), (1,0) (2,4) (4,2) (4,6) (6,4)}

stuck on both of these (btw it's that p isn't the letter p it's a logic symbol