Answer
a) Simplification
b) Disjunctive Syllogism
c) Modus Ponens
d) Addition
e) Hypothetical Syllogism
Work Step by Step
a) Let us assume:
q="Kangaroos live in Australia"
p="Kangaroos are marsupials"
We can write the given argument using above stated interpretation as:
$p \land q$
$∴p$
Note that the argument uses rule of simplification.
b) Let us assume:
q="The pollution is dangerous"
p="It is hotter than 100 degrees outside today"
We can write the given argument using above stated interpretation as:
$p \lor q$
$\neg p$
$∴ \neg p$
Note that the argument uses rule of Disjunctive Syllogism
c) Let us assume:
p="If Linda is an excellent swimmer"
q="She can work as a lifeguard"
We can write the given argument using above stated interpretation as:
$p \lor q$
$p$
$∴ q$
Note that the argument uses rule of Modus Ponens.
d) Let us assume:
p="This summer Steve will work at a computer company "
q="He will be a beach bum"
We can write the given argument using above stated interpretation as:
$p$
$p \lor q$
Note that the argument uses rule of Addition.
e) Let us assume:
p="I work all night on this homework"
q="I answer all the exercises"
r="I will understand the material"
We can write the given argument using above stated interpretation as:
$p \to q$
$q \to r$
$∴ p \to r$
Note that the argument uses rule of Hypothetical Syllogism.
