rec0614_key

# rec0614_key - COT3100 Summer2001 Recitation on relations...

This preview shows pages 1–2. Sign up to view the full content.

COT3100 Summer’2001 Recitation on relations (Solutions) 06/14/2001 1. Let A ={1, 2, 3}, B ={1, 2, 3, 4}, and R 1 ={(1,2), (2,2), (3,3)} and R 2 = {(1,2), (1, 3), (1,4)} are relations from A to B . Find R 1 R 2 , R 1 R 2 , R 1 - R 2 , R 2 - R 1 . R 1 R 2 = {(1, 2), (2, 2), (1, 3), (1, 4), (3, 3)} R 1 R 2 = {(1, 2)} R 1 - R 2 = {(2, 2), (3, 3)} R 2 - R 1 = {(1, 3), (1, 4)} 2. Given the set A = {2, 3, 4, 8, 9, 12, 18}, define a relation T over A such that T = {( a , b )| a A and b A and ab is a square number, i.e., ab = c 2 for some integer c }. Answer the following two questions. a) Use a directed graph to depict the relation T defined above. b) Determine if relation T satisfies each of the properties: irreflexive, symmetric, and transitive. Not irreflexive (it is reflexive) symmetric transitive 3. Suppose R and S are symmetric binary relations on a set A. Must the following relations be symmetric? Give either proofs or counterexamples to justify your answers. a) R S Proof. Assume ( x , y ) is arbitrary element from R S , i. e. ( x , y ) R S . We need to prove that ( y , x ) R S given R and S are symmetric. If ( x , y ) R S , then ( x , y )

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This document was uploaded on 07/14/2011.

### Page1 / 2

rec0614_key - COT3100 Summer2001 Recitation on relations...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online