Let s be the set of people in the united states. test the following binary relations on s for reflexivity, symmetry, antisymmetry, and transitivity.
a. x rho y > x is the husband of y.
b. x rho y > x is the spouse of y.
c. x rho y > x has the same parents as y.
d. x rho y > x is the brother of y.

Step-by-step explanation:

a. x rho y ---> x is the husband of y.

Not reflexive, because x cannot be husband of x, not symmetric also not transitive

b. x rho y ---> x is the spouse of y.

Not reflexive, but symmetric because when x is the spouse of y, y is the spouse of x.  Canot be transitive

c. x rho y ---> x has the same parents as y.

This is reflexive, symmetric and also transitive.  Because when x and y have same parents and y,z have same parents then x and z have same parents.

d. x rho y ---> x is the brother of y

Not reflexive, need not be symmetric if x is a girl.

Transitive is true.

don't know sorry bru

step-by-step explanation:

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.