Answer:
a) Addition b) Simplification c) Modus Ponens d) Modus Tollens e) Hypothetical Syllogism
Step-by-step explanation:
Firstly before applying the Rules of Inference, we have to translate those arguments into a symbolic form.
a) Alice is a mathematics major. Therefore, Alice is either a mathematics major or a computer science major.
Alice is a mathematics major = B
A computer Science major = R
1. P
2. ∴P ∨ Q
3. P→(P ∨ Q)
What we have here is a corresponding Tautology called Addition
Addition
b) Jerry is a mathematics major and a computer science major. Therefore, Jerry is a mathematics major.
Making the whole process of translating into symbolic language.
1. Jerry is a mathematics major and a computer science major: P ∧ Q
2. P
3 (P∧Q)→(P)
Since those premises in 1 and 2 are composed by and implication and a conjuction, this corresponding tautology is a
Simplification.
c) If it is rainy, then the pool will be closed. It is rainy. Therefore, the pool is closed.
Decomposing the premises and translating into Symbolic:
. it is rainy= P. the pool closed= Q
1st. Premise: P→Q
2nd. P
3rd. (P→Q. ∧P)→Q
Notice these Corresponding Tautologies. How they reinforce the argument, making it valid.
Modus Ponens
d) If it snows today, the university will close. The university is not closed today. Therefore, it did not snow today.
It snows today =P
The university will close=Q.
The university is not closed=¬Q
it did not snow today=¬P
1. (P→Q)
2.∧¬Q
3. ¬P
4.((P→Q)∧ ¬Q)→¬P
Modus Tollens
e) If I go swimming, then I will stay in the sun too long. If I stay in the sun too long, then I will sunburn. Therefore, if I go swimming, then I will sunburn.
I go swimming= P, I will stay in the sun too long= Q
I stay in the sun too long = R I will sunburn=S
1: P→Q
2:R→S
3. P→S
(P→Q)∧(R→S)→(P→S)
Hypothetical Syllogism
