Law of inferences Here are the symbols of various logical operators as I use them on this website (there is no one, universal list of symbols, though certain norms are adhered to across the spectrum): ∧ = And ∨ = Or → = If…then ¬ = Not (negation) ≡ = Logical Equivalence Here are the most common inferences in symbolic logic: 1) Modus Ponens (MP) P → Q P Therefore, Q 2) Modus Tollens (MT) P → Q ¬Q Therefore, ¬P 3) Hypothetical Syllogism (HS) P → Q Q → R Therefore, P → R 4) Disjunctive Syllogism (DS) P ∨ Q ¬P Therefore, Q 5) Simpliļ¬cation (SIMP) P ∧ Q Therefore, P 6) Addition (ADD) P Therefore, P ∨ Q 7) Double Negation (DN) P Therefore, ¬¬P 8) Conjunction (CONJ) P Q Therefore, P ∧ Q 9) Constructive Dilemma (CD) (P → Q) ∧ (R → S) P ∨ R Therefore, Q ∨ S 10) Destructive Dilemma (DD) (P → Q) ∧ (R → S) ¬Q ∨ ¬S Therefore, ¬P ∨ ¬R Finally, here are the 9 logical equivalences: 1) De Morgan’s Theorem (DeM) ¬(P ∧ Q) ≡ ¬P ∨ ¬Q ¬(P ∨ Q) ≡ ¬P ∧ ¬Q 2) Commutation (Comm) (P ∨ Q) ≡ (Q
Irving Copi Hello, my self Sujit Sarkar, a mathematics student from Visva-Bharati University, when we were taking this course in 3rd semester we faced many problems such as how to check my answers so I have decided to create this blog hope it is helpful to all of the students of our university as well as other students who are following this book for this course. First, let's discuss some basic questions which will help us to start this course. 1) What is logic? Logic is the study of the methods and principles used to distinguish correct from incorrect reasoning. 2) Why do we need? When someone wants to make judgments that can be completely relied upon, their only solid foundation will be correct reasoning. Using the methods and techniques of logic—one can distinguish reliably between sound and faulty reasoning. 3) What is Proposition? A statement; what is typically asserted using a declarative sentence, and hence always either true or false—alth