Alex feels sick, so he walks to Vanderbilt\'s Student Healthcarecenter. The nurse proceeds to identify some unusual symptomsappearing on Alex\'s body. During the nurse\'s questioning, Alexremarks that he attends regular classes with a small group offriends, but none of his friends have the same symptoms as Alex.After the initial screening, the nurse inputs the following twoitems into the computer system regarding Alex\'s situation.

(i) Alex may have eitherCOVID or the monkeypox virus.

(ii) Alexhas flu-like symptoms andskin rashes on the body.

A doctor sees Alex shortly after that and uses the following twoknowledge bases to conclude that Alex caught the monkeypox virus(author\'s note: The following two statements are not necessarily\"medically\" accurate, so don\'t use them as a basis for yourhealthcare).

(iii) If a person hasskin rashes, the viruscannot transmit from human to human veryefficiently.

(iv) If a person has tested positivefor COVID or breathes aircontaining the COVID virus, the viruscan transmit from human to human veryefficiently.

1. [2 POINTS]. Using the bolded words from i-ivabove, complete the table with the list of predicates and theirmeaning. The first one has been completed for you.

Predicate	Proposition
C(x)	C = The student x has tested positive for COVID.
M(x)
F(x)
R(x)
T(x)
B(x)

Exercise #3 (continued)

1. [2 POINTS]. Translate each proposition fromthe original text into symbolic logic using the above propositions.You do not need to use quantifiers but be sure toindicate any predicates.

1. Alex has eitherCOVID or monkeypoxvirus.

1. Alex has flu-like symptoms andskin rashes on the body.

1. If a person such as Alex has skin rashes,the virus cannot transmit from human tohuman very efficiently.

(iv) If a person such as Alexhas already tested positivefor COVID or breathes aircontaining the covid virus, thevirus transmits from human to human veryefficiently.

Exercise #3 (continued)

1. [8 POINTS]. Based on the nurse\'s comments andknowledge bases from parts i-iv, you are to prove the doctorconcluded the student has monkeypox. In otherwords, we want to prove that the statements from 1 to 4 in part Bleads to the conclusion: \"Therefore, Alexhas monkeypox.\"

1. [2 POINTS] First, state below the full WFF(i.e., well-formed formula) that you are attempting to prove. Forthis part, you may simplify the syntax to list just the relevantcapital letter. For example, you can use \"B\" instead of B(x):

WFF [2 POINTS]:

1. [6 POINTS] Next, using the table below, writeyour proof using the rules of propositional logic. Be sure to listeach of the above premises separately on a line at the start of theproof. Include a justification for each step of the proof. Forexample, if you used Modus Ponens based on a statement from line 5,you would write \"5, MP\" as your justification on the current line.Again, you may simplify the syntax to include the relevant capitalletter. For example, you can use \"B\" instead of B(x). You may notneed all the lines provided below.

#	Statement	Justification
1
2
3
4
5
6
7
8
9
10
11
12