Week 15.pdf

# Week 15.pdf - MAT 243 Week 15/15 Written Homework 1...

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MAT 243 Week 15/15 Written Homework 1. Consider the not equal 6 = relation on the integers. (a) Prove that 6 = is not transitive. Proof. We need to show that there exist integers a , b and c such that ( a, b ) 6 = and ( b, c ) 6 = but ( a, c ) / 6 =. Let a = 1, b = 2 and c = 1. Then (1 , 2) 6 = and (2 , 1) 6 = but (1 , 1) / 6 =. (b) Prove that 1 6 = 2 1. Proof. Since (1 , 2) 6 = and (2 , 1) 6 =, (1 , 1) 6 = 2 by definition of the squared relations. 2. Based on your experience in problem 1b, you may suspect that if a relation R on S is symmetric, then R 2 is reflexive. Prove of disprove this.
• Spring '14
• RochusBoerner
• Legal burden of proof, Transitive relation, ASU School of Mathematical and Statistical Sciences, R. Boerner

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