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Logical Equivalences Quiz

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Questions and Answers

Which logical connective represents the logical operation of 'OR' in the expressions?

∧
↔
¬
∨ (correct)

What does the expression (p → q) ↔ (¬p → ¬q) represent?

Disjunctive syllogism
Conditional equivalence
Contrapositive relationship (correct)
Negation of conjunction

In the expression (p ∨ ¬(p ∧ q)), what is the effect of the negation (¬) on the conjunction (p ∧ q)?

It makes it always true
It acts as a conjunction
It negates the entire conjunction (correct)
It negates only p

What is the logical implication of the expression ((a ∨ b) ∧ (a → c) ∧ (¬b → c)) → c?

<p>c must be true if a or b is true (A)</p> Signup and view all the answers

What does the expression (p ∨ q) → ¬r imply in terms of r?

<p>If either p or q is true, then r must be false (A)</p> Signup and view all the answers

Flashcards

Logical Expression 1

p or not(p and q)

Logical Expression 2

If p then q, is equivalent to if not p then not q

Logical Expression 3

(p or q) implies not r

Logical Expression 4

(a or b and a implies c and not b implies c) implies c

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Propositional Logic

A branch of logic that deals with statements of truth values, using logical connectives.

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Logical Connectives

Symbols that connect propositions, like OR, AND, NOT, implication or biconditional.

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Study Notes