Discrete Structures Question: Four robots enter a race. Marv, Rae, Dex, and Ty$.$ The robots each finish in a distinct

position, no ties. Given the following information, answer the subsequent questions:

One of the robots finishes between Rae and Lex.

Two of the robots finish between Lex and Ty$.$

Rae doesn't finish second.

a$.$ Write the sets for robots and possible placing and define them as variables.

b$.$ What are the cardinalities of these sets?

c$.$ What is the power set of the positions?

d$.$ Declare a general quantifier that takes in $(x,y,z)$ to handle the first two statements.

e$.$ Declare four non$-$disjunctive sets for each character $A(x),$ starting with all possibilities for

each, you will update these as you move forward.

f$.$ Declare a proposition using the input values for the first statement.

g$.$ Declare a proposition for the second statement.

h$.$ Declare a proposition for the third statement.

i$.$ Write a logical statement that is true to prove the system result.

j$.$ Using the information above, write a proof of the solution. As you move through the $3$

proposition statements in your proof, you should update the non$-$disjunctive sets until they

all have a single value, rendering them disjunctive sets.