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.

q: 92 degrees

hope i ^-^

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.