Question

of the following relations is the antisymmetric and transitive relation over the set {1, 2, 3}? a) {(1,1), (3,2), (2,1),(2,2)} b) {(1,1), (2,2)} c) {(1,1), (2,2), (1,2), (2,3), (2,1), (1,3)} d) { (1,2), (4,3), (2,3), (1,3)}

          of the following relations is the antisymmetric and transitive relation over the set {1, 2, 3}?

a) {(1,1), (3,2), (2,1),(2,2)}
b) {(1,1), (2,2)}
c) {(1,1), (2,2), (1,2), (2,3), (2,1), (1,3)}
d) { (1,2), (4,3), (2,3), (1,3)}

Added by Marie R.

Elementary and Intermediate Algebra

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

Instant Answer

Solved by Expert Supreeta N

05/20/2023

Step 1

A relation R on a set A is antisymmetric if for all (a, b) and (b, a) in R, a = b. In other words, if (a, b) and (b, a) are both in R, then a must be equal to b. A relation R on a set A is transitive if for all (a, b) and (b, c) in R, (a, c) is also in R. In Show more…

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of the following relations is the antisymmetric and transitive relation over the set {1, 2, 3}? a) {(1,1), (3,2), (2,1),(2,2)} b) {(1,1), (2,2)} c) {(1,1), (2,2), (1,2), (2,3), (2,1), (1,3)} d) { (1,2), (4,3), (2,3), (1,3)}