Logic

Fundamental Concepts of Logic

• Propositions: These are statement that are either true or false, but not both.
• Logical Connectives: These include and (∧), or (∨), not (¬), implies (→), and if and only if (↔), used to connect propositions.

Truth Tables

• A Truth Table is a mathematical table that illustrates the possible outcomes of a logical expression based on the various possible values of its variables. Truth tables are fundamental in logic.

Logical Equivalence

• Two propositions are said to be logically equivalent if their truth tables are identical.
• Logical equivalence is often used to simplify complex expressions.

Logical Inference

• Inference is the process of deriving logical conclusions from premises known or assumed to be true.
• Common forms of inference used in logic include modus ponens, modus tollens, hypothetical syllogism, disjunctive syllogism, addition, simplification, and conjunction.

Laws of Logic

• Certain laws or rules govern operations in logic. They include the commutative laws, associative laws, distributive law, law of identity, law of nullity, law of double negation, De Morgan’s laws, etc.

Remember, understanding how to apply these concepts and principles of logic is as important as understanding the fundamentals themselves. Practice and analysis of varied problems are key to mastering the topic of logic.