Rules of Inference - Definition & Types of Inference Rules

Discrete Mathematics: Rules of Inference in Propositional Logic - Definition & Types of Inference Rules
Topics discussed:
1. Meaning of Inference.
2. Definition of Rules of Inference.
3. Following types of Inference Rules:
a. Modus Ponens.
b. Modus Tollens.
c. Hypothetical Syllogism.
d. Disjunctive Syllogism.
e. Addition.
f. Simplification.
g. Conjunction.
h. Resolution.
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About rules of inferences, do we only consider true premises? For example, the Addition rule, I worked the truth table for p, q and pVq, and it doesn't imply the implication -> (if... then...) truth table.

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Interesting that there exists more rules of inference that are not introduced in Patrick J. Hurley's books.

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For modus ponens and modus tollens 1:15

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Is converse possible for addition rule and simplification rule?

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Why you decided that p is T or a is T in the begin . For ex . in modus ponens you said in the begin , that p is true and p imply q is true

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Show that the following arguments are valid using the rule of reference and logical laws?
a)Premises are (¬p → (r ∧¬s) , t → s , u → ¬p, ¬w, u ∨ w), Conclusion is (¬t)?
Can anyone solve this for me I need to prepare myself for exam. Thank you.

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Yeah but no...the implication Boolean expression in particular is actually not an accurate representation of our everyday "statement --> it's implication" kind of sentences or scenarios.
On the surface, these expressions might look the same and appear to be corresponding to real life scenarios but at one point they could get too abstract and detached from what seems to be reality for us from our common-sense influenced viewpoint so...yeah, don't approach them using common sense.
The whole point of the entire discipline of logic, a subset of discrete maths, is to question and challenge our common sense.

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