Comlete question is;
Given the following relations on the set of all people. Check ALL correct answers from the following lists:
(a) a is older than b;
A. antisymmetric
B. irreflexive
C. transitive
D. reflexive
E. symmetric
(b) a and b have a common grandparent;
A. reflexive
B. symmetric
C. irreflexive
D. transitive
E. antisymmetric
(c) a has the same first name as b;
A. reflexive
B. irreflexive
C. transitive
D. symmetric
E. antisymmetric
(d) a and b were born on the same day;
A. symmetric
B. reflexive
C. transitive
D. antisymmetric
E. irreflexive
Answer:
a) Options A, B & D.
b) Options C & D.
c) Options C, D & E
d) Options A, B & C
Step-by-step explanation:
a) Options A, B & D.
- It's irreflexive because b is not older than a.
- It's transitive because if a is older than b as we are told and b is older than c, then we can say that a is older than c.
- It's antisymmetric because if a is older than b, then we can say that b is not older than a.
b) Options C & D.
- It's symmetric because if a & b have a common grandparent, then we can say that b and a have a common grandparent.
- It's reflexive because a and b have common grandparents and thus implies all of a's grandparents.
c) Options C, D & E are correct.
It could be Transitive, symmetric or antisymmetric.
d) Options A, B & C are correct.
