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Reflexive -- First sentence of proof is: Let x Z Let (x,x) R. Let (x,x) I Let x R. Symmetric -- First sentence of proof is: Let x Z Assume (x,y) R. Assume (y,x) R -1 . Let x R Let (x,y) R and (y,x) R.
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Reflexive -- First sentence of proof is: • Let x Z • Let (x,x)R. • Let (x,x) I • Let x R
Symmetric -- First sentence of proof is: • Let x Z • Assume (x,y)R. • Assume (y,x) R-1. • Let x R • Let (x,y) R and (y,x) R
Transitive -- First sentence of proof is: • Let x Z • Assume (x,y)R. • Assume (y,x) R-1. • Assume (x,y) R and (x,z) R • Assume (x,y) R and (y,z) R • Assume (x,y) R and (y,x) R
Reflexive -- First sentence of proof is: • Let (x,x) R2 • Let (x,y)R. • Let (x,x) R • Let x R • Let x R2 • Let (x,y) R2
Next sentence of proof is: • Assume R is symmetric. • Assume R = R-1. • Assume (x,y) R. • Assume x R. • Assume x A. • Assume (x,y) R-1.
Next sentence of proof is: • Assume R is symmetric. • Assume R = R-1. • Assume (x,y) R. • Assume x R. • Assume x A. • Assume (x,y) R-1.
Next sentence of proof is: • Assume R is symmetric. • Assume R = R-1. • Assume (x,y) R. • Assume x R. • Assume x A. • Assume (x,y) R-1.
Next sentence of proof is: • Assume R is symmetric. • Assume R = R-1. • Assume (x,y) R. • Assume x R. • Assume x A. • Assume (x,y) R-1.
Next sentence of proof is: • Assume R is symmetric. • Assume R = R-1. • Assume (x,y) R. • Assume x R. • Assume x A. • Assume (x,y) R-1.