Inference questions ask you to analyze the logical reasoning of an argument and determine what other information necessarily follows from it. To determine what necessarily follows, or flows, from the argument, you’ll need to learn formal logical reasoning inference rules. These rules are the backbone of an argument, and understanding them can refine your approach to question types we learned in earlier lessons.

Inference: A conclusion reached on the basis of evidence and reasoning.

Note how similar the definition of an inference is the definition of a conclusion:

Conclusion: A statement that necessarily follows from the stated and unstated premises.

Notice how a conclusion flows from the premises—or evidence—but an inference flows from evidence AND reasoning. So what does it mean to flow from reasoning? Let’s learn some formal logic:

Modus Ponens: a deductive reasoning inference rule of logic stating that if a conditional statement (“if p then q ”) is accepted, and the antecedent ( p ) holds, then the consequent ( q ) may be inferred.

Example: If I sit hunched over my desk, I will likely end up with back pain. I sat hunched over my desk for five hours. So, I may end up with back pain.

Symbolization:

P → Q

P

---------

Q

Modus Tollens: the inference rule of logic stating that if a conditional statement (“if p then q ”) is accepted, and the consequent does not hold ( not-q or ~q ), then the negation of the antecedent ( not-p or ~q) can be inferred.

Example: If I sit hunched over my desk, I will likely end up with back pain. I did not end up with back pain today. So I must have not sat hunched over my desk.

Symbolization:

P → Q

~Q

----------

~P

Modus Tollendo Ponens (aka disjunction syllogism): A valid form of argument in which the antecedent (p) of a conditional proposition (Either p or q) is negated (~p), thereby entailing the affirmation of the consequent (q).

Example: Either I am going to watch Bordertown on Netflix, or I’m going to watch The Good Fight because my eyes are too tired to handle the subtitles. My eyes are too tired for the subtitles in Bordertown, therefore, I’m going to watch The Good Fight.

Symbolization:

P v Q

~P

______

Q

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