The answers to exercises marked [BB] can be found in the Back of the Book.Answer Exercise...

The answers to exercises marked [BB] can be found in the Back of the Book.

Answer Exercise for each of the following relations:

(a) A = {1,2}; ={(1,2)}.

(b) [BB] A = {1,2, 3,4}; = {(1, 1), (1,2), (2, 1), (3,4)}.

(c) LBB] A = Z; (a, b) ∈ ft if and only if ab > 0.

(d) A = R; (a, b) ∈ ft if and only if fl2 = b2.

(e) A = R; (a, b) ∈ ft if and only if a − b ≤ 3.

(f) A = Z × Z; ((a, b), (c, d)) 6 ft if and only if a − c = b − d.

(g) A = N; (a, b) ∈ R if and only if a =# b.

(h) A = Z; R = {(x, y) \ x + y = 10}.

(i) [BBJ A = R2; R = {((x, y), (u, v)) | x + y ≤ u + v}.

(j) A = N; (a, b) ∈ it and only if | is an integer.

(k) A = Z; (a, b) ∈ R if and only if f is an integer.

The answers to exercises marked [BB] can be found in the Back of the Book.

Determine whether each of the binary relations defined on the given sets A is reflexive, symmetric, anti-symmetric, or transitive. If a relation has a certain property, prove this is so; otherwise, provide a counterexample to show that it does not.

(a) [BB] A is the set of all English words; (a, b) ∈ and only if a and b have at least one letter in common.

(b) A is the set of all people, (a, b) ∈ R. if and only if neither a nor b is currently enrolled at Miskatonic University or else both are enrolled at MU and are taking at least one course together.