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4 cards from this section. Quick, good the night before a test.
Define what a predicate is.
Think about how statements relate to variables.
What does the universal quantifier '∀x' signify?
Consider the meaning of 'for all' in logic.
What does the symbol '∀' represent in predicate logic?
Consider how we express 'all' in logical statements.
True or False: Existential quantification asserts that all elements are true for a predicate.
Think about the requirement for 'exist' versus 'all'.
Prove that '∀x (P(x) ∧ Q(x))' is logically equivalent to '∀x P(x) ∧ ∀x Q(x)'.
Use methods of logical equivalences and quantify simultaneously.
In a domain of natural numbers, evaluate the truth of '∃x (P(x)) → ∀x (Q(x))'. What implications does this carry?
Consider the implications of assuming P for all x and how it connects to the consequent.
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