What rule of inference is used in each of these arguments? a) Kangaroos live inAustralia and are marsupials. Therefore, kangaroos are marsupials. b) It is either hotter than 100 degrees today or the pollution is dangerous. It is less than 100 degrees outside today. Therefore, the pollution is dangerous. c) Linda is an excellent swimmer. If Linda is an excellent swimmer, then she can work as a lifeguard. Therefore, Linda can work as a lifeguard. d) Steve will work at a computer company this summer. Therefore, this summer Steve will work at a computer company or he will be a beach bum.

Simplification (also known as conjunction elimination) is an immediate argument form by which is inferred, for example, that if the conjunction A and B is true, then consequently A must be true, and B also must be true. Modus ponens means in Latin "mode that by affirming affirms", this being a mode of deductive reasoning and a rule of inference. A hypothetical syllogism is a valid argumentation mode in which a syllogism, i.e., deductive reasoning that arrives at a specific conclusion by analyzing two different premises, may have a conditional statement for one or both of these premises. A hypothetical syllogism is associated with modus ponens in the way that sometimes it is considered to be a double modus ponens. Addition is a rule of inference that enables the introduction of disjunctions into logical proofs. For example, the rule of addition states that if P is true, then consequently P or Q must be true.