A = {1, 3, 7, 9} and S be the binary relation on A defined by: x S y <=> x^3 ≡ y (mod 10) (a) State explicitly which ordered pairs are in S. (b) State explicitly which ordered pairs are in S^-1. (c) Is S reflexive? Yes or No? (circle one, no proofs.) (d) Is S symmetric? Yes or No? (circle one, no proofs.) (e) Is S transitive? Yes or No? (circle one, no proofs.)

Question

Let A = {1, 3, 7, 9} and S be the binary relation on A defined
by: x S y <=>
x^3 ≡ y (mod 10)
(a) State explicitly which ordered pairs are in S.
(b) State explicitly which ordered pairs are in S^-1.
(c) Is S reflexive? Yes or No? (circle one, no proofs.)
(d) Is S symmetric? Yes or No? (circle one, no proofs.)
(e) Is S transitive? Yes or No? (circle one, no proofs.)

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