# am_lect_05 - Announcements HW due TODAY next HW released...

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Announcements HW due TODAY, next HW released TODAY

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Predicates and Variables A predicate is a statement that becomes a proposition when we substitute values for all variables . Examples : x 2 < 10” or “My current grade in course x is y We use the notation P ( x ) to denote predicate P with variable x Q ( x , y ) denotes a predicate with two variables Given a predicate P ( x ), we can ask two kinds of questions: — Is there a value for variable x for which P ( x ) is true? — Is P ( x ) true for all possible values of x ? In both cases, an important point will be: what possible values can x take?
Existential Quantifier ( ) Consider: “There is some rational number whose square is 2.25” In symbols, we say: x Q , x 2 = 2.25 — there exists a rational number x such that x 2 = 2.25 — there exists at least one such rational number (actually two) — If we want to say “there exists exactly one x …” we say ! x Example

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am_lect_05 - Announcements HW due TODAY next HW released...

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