Let A = Z+ Z+. Define a relation R on A as follows: For all (a, b) and (c, d) in A, (a

Chapter 8, Problem 44

(choose chapter or problem)

Let A = \(\mathbf{Z}^{+} \times \mathbf{Z}^{+}\). Define a relation R on A as follows: For all (a, b) and (c, d) in A,

(a, b) R (c, d) \(\Leftrightarrow\) a + d = c + b.

a. Prove that R is reflexive.

b. Prove that R is symmetric.

c. Prove that R is transitive.

d. List five elements in [(1, 1)].

e. List five elements in [(3, 1)].

f. List five elements in [(1, 2)].

g. Describe the distinct equivalence classes of R.

Text Transcription:

Z^+ times Z^+

Leftrightarrow