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Logic and propositional calculus. ( a ) ( 5 points ) Basic definitions and properties ( propositions and compound propositions; logical operators on propositions; converse

Logic and propositional calculus.
(a)(5 points) Basic definitions and properties (propositions and compound propositions; logical operators on propositions; converse proposition; contrapositive proposition; inverse proposition; equivalent propositions; biconditionals; truth tables; precedence of logical operators; consistent system; tautology; contradiction; satisfiable proposition; predicatcs; quantifiers). Give an exhaustive definition of each notion.
(b)(5 points) Related theorems (applications of propositional logic; De Morgan's laws; main logical equivalences; logical equivalences involving conditional and biconditional statements; negating quantified expressions). Demonstrate your understanding of these theorems by examples.
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