Try the fastest way to create flashcards
Question

# Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a, b) ∈ R if and only ifa) a is taller than b.b) a and b were born on the same day.c) a has the same first name as b.d) a and b have a common grandparent.

Solution

Verified
3.9 (14 ratings)
3.9 (14 ratings)
Step 1
1 of 6

DEFINITIONS

A relation $R$ on a set $A$ is $\textbf{reflexive}$ if $(a,a)\in R$ for every element $a\in A$.

A relation $R$ on a set $A$ is $\textbf{symmtric}$ if $(b,a)\in R$ whenever $(a,b) \in R$

A relation $R$ on a set $A$ is $\textbf{antisymmtric}$ if $(b,a)\in R$ and $(a,b) \in R$ implies $a=b$

A relation $R$ on a set $A$ is $\textbf{transitive}$ if $(a,b)\in R$ and $(b,c) \in R$ implies $(a,c)\in R$

## Recommended textbook solutions

#### Discrete Mathematics and Its Applications

7th EditionISBN: 9780073383095 (8 more)Kenneth Rosen
4,283 solutions

#### Discrete Mathematics

8th EditionISBN: 9780321964687Richard Johnsonbaugh
4,246 solutions

#### Discrete Mathematics and Its Applications

8th EditionISBN: 9781259676512 (3 more)Kenneth Rosen
4,397 solutions

#### Discrete Mathematics with Applications

5th EditionISBN: 9781337694193Susanna S. Epp
2,641 solutions