Relations

Question 1

Reflexive

Answer 1

When everything in the domain is beared to the one subject, so when it includes itself. For example, ‘x has the same blood group as y’ includes x because it has to have the same blood group

Question 2

Irreflexive

Answer 2

When nothing in the domain is beared to the one subject, so when the statement does not include itself. For example, ‘x is y’s father’ because the statement cannot ring true for x because x cannot be its own father.

Question 3

Neither reflexive nor irrelfexive

Answer 3

Does not definitely fall into either category, is not objectively including itself or not. For example, ‘x thinks y is good-looking’ is neither reflexive or irreflexive because some people think themselves are good-looking and others do not.

Question 4

Symmetric

Answer 4

If the subject holds x to y, it will also hold for y to x. The statement works when flipped around too. For example, ‘x is y’s cousin’ also works as ‘y is x’s cousin’

Question 5

Asymmetric

Answer 5

If the subject that holds x to y does not hold y to x. The statement does not remain true when the subjects are swapped around. For example, ‘x is the father of y’ does not work when you say ‘y is the father of x’.

Question 6

Neither symmetric or asymmetric

Answer 6

When the subject does not fall into either of the above, there is no definitive way to say that it is symmetric or asymmetric. For example, ‘x is the sister of y’ is not certainly symmetric because we do not know the gender of the subject, this means we cannot say if it is asymmetric either so it is neither.

Question 7

Transitive

Answer 7

When the subject that holds between x and y and y and z, will also hold true between x and z. For example, if x is a descendant of y and y is a descendant of z then x must also be a descendant of z.

Question 8

Intransitive

Answer 8

When the subject that holds between x and y and y and z does not hold between x and z. For example, if x is the complimentary colour to y, y is also the complimentary colour to x, however, x cannot be the complimentary colour to z. This works with opposites, and fathers and grandfathers, eg. if x if the father of y, y can be the father or z but x cannot be the father of z.