Answer
a) Addition
b) Simplification
c) Modus Ponens
d) Modus Tollens
e) Hypothetical Syllogism
Work Step by Step
a) Let us assume:
p="Alice is a mathematics major"
q="Alice is a computer science major"
We can write the given argument using above stated interpretation as:
$$p$$$$- - -$$$$p \lor q$$
Using Rule of addition
b) Let us assume:
p="Jerry is a mathematics major"
q="Jerry is a computer science major"
We can write the given argument using above stated interpretation as:
$$p \land q$$$$- - -$$$$\therefore p$$
Note that the argument uses rule of simplification.
c) Let us assume:
p="It is rainy"
q="pool will be closed"
We can write the given argument using above stated interpretation as:
$$p \to q$$$$p$$$$- - -$$$$q$$
Note that the argument uses rule of Modus Ponens.
d) Let us assume:
p="It snows today"
q="University is closed"
We can write the given argument using above stated interpretation as:
$$p \to q $$$$\neg q$$ $$- - -$$ $$\therefore \neg p$$
Note that the argument uses rule of Modus Tollens.
e) Let us assume:
p="I go swimming"
q="I will stay in the sun too long"
r="I will sunburn"
We can write the given argument using above stated interpretation as:
$$p \to q$$$$q \to r$$$$- - - $$$$\therefore p \to r$$
Note that the argument uses rule of Hypothetical Syllogism.
