Logic and Proofs Flashcards

Flashcards about Logic and Proofs

What is a proposition?

A sentence that can be either true or false.

What are the three connectives used in propositional forms?

Conjunction (∧), disjunction (∨), and negation (~).

When is the conjunction of P and Q (P ∧ Q) true?

P and Q is true.

When is the disjunction of P and Q (P ∨ Q) true?

At least one of P or Q is true.

When is the negation of P (~P) true?

P is false.

When are two propositional forms considered equivalent?

They have the same truth values for all possible truth assignments to their variables.

In the absence of parentheses, what is the order of operations for connectives?

Apply connectives in the order: negation, conjunction, disjunction.

What is a tautology?

A propositional form that is always true.

What is a contradiction?

A propositional form that is always false.

What is a denial of a proposition P?

A proposition that is true only when P is false, and vice versa.

Example of applying DeMorgan’s Laws to negate the statement 'x is odd or x ≤ 2'?

The negation of 'x is odd or x ≤ 2' is 'x is even and x > 2'.