# relfexive ,symmetric & transitive

• Nov 13th 2012, 08:15 AM
franios
relfexive ,symmetric & transitive
Give an example of a relation that is:
a) relfexive and symmetric but not transitive
b) symmetric and transitive but not reflexive
c)reflexive and transitive but not symmetric
• Nov 13th 2012, 08:30 AM
abender
Re: relfexive ,symmetric & transitive
Quote:

Originally Posted by franios
Give an example of a relation that is:
a) relfexive and symmetric but not transitive

Reflexive: A has showered with A.
Symmetric: A has showered with B implies B has showered with A.
Transitive: A has showered with B and B has showered with C does NOT imply that A has showered with C.
• Nov 13th 2012, 08:36 AM
abender
Re: relfexive ,symmetric & transitive
Quote:

Originally Posted by franios
Give an example of a relation that is:
b) symmetric and transitive but not reflexive

Reflexive: A is NOT a full sibling to A.
Symmetric: A is a full sibling to B implies B is a full sibling to A.
Transitive: A is a full sibling to B and B is a full sibling to C implies that A is a full sibling to C.
• Nov 13th 2012, 08:42 AM
abender
Re: relfexive ,symmetric & transitive
Quote:

Originally Posted by franios
Give an example of a relation that is:
c)reflexive and transitive but not symmetric

Reflexive: $\displaystyle A\leq A$.
Symmetric: $\displaystyle A\leq B$ does NOT imply $\displaystyle B\leq A$.
Transitive: $\displaystyle A\leq B$ and $\displaystyle B\leq C$ implies $\displaystyle A\leq C$.