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Reflexive -- First sentence of proof is: (1) Let x Z (2) Let (x,x) R. (3) Let (x,x) I (4) Let x R
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Symmetric -- First sentence of proof is: (1) Let x Z (2) Assume (x,y) R. (3) Assume (y,x) R -1. (4) Let x R (5) Let (x,y) R and (y,x) R
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Transitive -- First sentence of proof is: (1) Let x Z (2) Assume (x,y) R. (3) Assume (y,x) R -1. (4) Assume (x,y) R and (x,z) R (5) Assume (x,y) R and (y,z) R (6) Assume (x,y) R and (y,x) R
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Reflexive -- First sentence of proof is: (1) Let (x,x) R 2 (2) Let (x,y) R. (3) Let (x,x) R (4) Let x R (5) Let x R 2 (6) Let (x,y) R 2
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Next sentence of proof is: (1) Assume R is symmetric. (2) Assume R = R -1. (3) Assume (x,y) R. (4) Assume x R. (5) Assume x A. (6) Assume (x,y) R -1.
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Next sentence of proof is: (1) Assume R is symmetric. (2) Assume R = R -1. (3) Assume (x,y) R. (4) Assume x R. (5) Assume x A. (6) Assume (x,y) R -1.
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Next sentence of proof is: (1) Assume R is symmetric. (2) Assume R = R -1. (3) Assume (x,y) R. (4) Assume x R. (5) Assume x A. (6) Assume (x,y) R -1.
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Next sentence of proof is: (1) Assume R is symmetric. (2) Assume R = R -1. (3) Assume (x,y) R. (4) Assume x R. (5) Assume x A. (6) Assume (x,y) R -1.
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Next sentence of proof is: (1) Assume R is symmetric. (2) Assume R = R -1. (3) Assume (x,y) R. (4) Assume x R. (5) Assume x A. (6) Assume (x,y) R -1.
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