anonymous
  • anonymous
Determine whether the relation R on the set of all people is reflexive, symmetric, anti- symmetric, and/or transitive, where (a, b) ϵ R if and only if a is taller than b.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Recall reflexivity means that our relation is true between an element and itself; equality of integers is reflexive because we know for any integer \(n\) that \(n=n\) (this is an axiom that the most basic math such as elementary algebra necessitates). Consider our relation, though; if we take any person, can you say he is taller than himself? That seems paradoxical, no?
anonymous
  • anonymous
Yes it does
anonymous
  • anonymous
Consider our next property, symmetry, which says that if an element a is related to b by our relation, then b must be similarly related to a by our relation. If we two people, say Alice and Bob, and we know Alice is strictly taller than Bob, does that mean Bob is strictly taller than Alice? This, too, makes very little sense!

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Anti-symmetry states that if we know Alice is taller than Bob for *any* Alice and *any* Bob, then we also know that Bob is NOT taller than Alice. This makes a lot more sense, surely!
anonymous
  • anonymous
yes it does.
anonymous
  • anonymous
Transitivity is another neat property; essentially, if we know Alice is taller than Bob, and Bob is taller than Eve, surely we can infer, then, that Alice is taller than Eve? This is *transitivity*.
anonymous
  • anonymous
... so all in all, we've concluded the relation 'taller than' is neither reflexive nor symmetric but is indeed anti-symmetric and transitive. Neat.
anonymous
  • anonymous
Okay

Looking for something else?

Not the answer you are looking for? Search for more explanations.