Question

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. symmetric B. irreflexive C. reflexive D. antisymmetric E. transitive

Answer 1

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.