Question

S. Prove by element chasing (i) if R, S are symmetric then so is $R \cup S$ (ii) if R, S are anti-symmetric then so is $R \cap S$ (iii) if R is transitive then so is $R^{-1}$ (iv) if R irreflexive and symmetric then it is not transitive (v) if R is reflexive and transitive then $R \circ R = R$.

          S. Prove by element chasing
(i) if R, S are symmetric then so is $R \cup S$
(ii) if R, S are anti-symmetric then so is $R \cap S$
(iii) if R is transitive then so is $R^{-1}$
(iv) if R irreflexive and symmetric then it is not transitive
(v) if R is reflexive and transitive then $R \circ R = R$.

S. Prove by element chasing
(i) if R, S are symmetric then so is R ∪ S
(ii) if R, S are anti-symmetric then so is R ∩ S
(iii) if R is transitive then so is R^-1
(iv) if R irreflexive and symmetric then it is not transitive
(v) if R is reflexive and transitive then R ∘ R = R.

Added by Patricia C.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Adi S

11/30/2022

Step 1

Step 1: To prove that R ∪ S is symmetric if R and S are symmetric, we need to show that for any (a, b) in R ∪ S, (b, a) is also in R ∪ S. Show more…

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Prove by element chasing (i) if R, S are symmetric then so is R ∪ S (ii) if R, S are anti-symmetric then so is RS (iii) if R is transitive then so is R (iv) if R is irreflexive and symmetric then it is not transitive (v) if R is reflexive and transitive then R o R = R