Given that T is a relation on the set {1, 2, 3, 4}, and the set of ordered pairs is: T = {(1, 1), (1, 2), (1, 4), (2, 1), (2, 3), (3, 2), (3, 3), (3, 4), (4, 1), (4, 3), (4, 4)}. Is T symmetric, ani-symmetric and/or transitive? Can you explain why?

Let X=\{a,b,c,d,e,f\}X={a,b,c,d,e,f} and SS be the relation on XX defined by S = \{ (a,a), (a,b), (a,c),S={(a,a),(a,b),(a,c), (a,d), (a,e), (a,f),(a,d),(a,e),(a,f), (b,b), (b,d), (b,e),(b,b),(b,d),(b,e), (b,f), (c,c), (c,d),(b,f),(c,c),(c,d), (c,e), (c,f), (d,d),(c,e),(c,f),(d,d), (d,e), (d,f), (e,e), (f,f) \}(d,e),(d,f),(e,e),(f,f)}. Is SS a partial order? If so, draw its Hasse diagram. If not, give an example showing why.