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

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.

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.

Quote:

---

Originally Posted by franios

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

---

Reflexive: .
Symmetric: does NOT imply .
Transitive: and implies .