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Consider the following two statements: 1. Everything is awesome! 2. Everything is cool when you're part of a team. Part A Translate both of these statements into expressions of predicate logic, using the following predicates: b A(x): x is awesome! C(y): y is cool. P(z, t): person z is part of team t. ● ● ● Hint: In English, the construction "q when p" can be rephrased as "if p then q." Your solution should therefore include →. 1) ** (A): A(X) 2) ZEC :((y) Part B The contrapositive of the implication p q is the statement -q p. Compute the contrapositive of your answer for the second statement in Part A. Please simplify your results so that negation symbols - appear directly in front of predicates, and not quantifiers or parenthetical expressions. So, an expression like -V: P(x) needs further simplification, as does 3y: (P(y) V Q(y)). Please show your steps.

Consider the following two statements: 1. Everything is awesome! 2. Everything is cool when you're part of a team. Part A Translate both of these statements into expressions of predicate logic, using the following predicates: b A(x): x is awesome! C(y): y is cool. P(z, t): person z is part of team t. ● ● ● Hint: In English, the construction "q when p" can be rephrased as "if p then q." Your solution should therefore include →. 1) ** (A): A(X) 2) ZEC :((y) Part B The contrapositive of the implication p q is the statement -q p. Compute the contrapositive of your answer for the second statement in Part A. Please simplify your results so that negation symbols - appear directly in front of predicates, and not quantifiers or parenthetical expressions. So, an expression like -V: P(x) needs further simplification, as does 3y: (P(y) V Q(y)). Please show your steps.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter10: Inequalities
Section10.3: Solving Problems Involving Inequalities
Problem 28E
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How do I translate these into logical expressions and then negate them?

Consider the following two statements: 1. Everything is awesome! 2. Everything is cool when you're part of a team. a • C(y): y is cool. P(z, t): person z is part of team t. 0000 1020 Part A Translate both of these statements into expressions of predicate logic, using the following predicates: A(x): x is awesome! x 1) ** (A): A(X) 2) FZ 6 C = C(y) Ha ADH Hint: In English, the construction "q when p" can be rephrased as "if p then q." Your solution should therefore include →. 120 2 di 201 Part B The contrapositive of the implication p q is the statement q→ p. Compute the contrapositive of your answer for the second statement in Part A. Please simplify your results so that negation symbols appear directly in front of predicates, and not quantifiers or parenthetical expressions. So, an expression like -Vx: P(x) needs further simplification, as does By: (P(y) V Q(y)). Please show your steps. 7
Transcribed Image Text:Consider the following two statements: 1. Everything is awesome! 2. Everything is cool when you're part of a team. a • C(y): y is cool. P(z, t): person z is part of team t. 0000 1020 Part A Translate both of these statements into expressions of predicate logic, using the following predicates: A(x): x is awesome! x 1) ** (A): A(X) 2) FZ 6 C = C(y) Ha ADH Hint: In English, the construction "q when p" can be rephrased as "if p then q." Your solution should therefore include →. 120 2 di 201 Part B The contrapositive of the implication p q is the statement q→ p. Compute the contrapositive of your answer for the second statement in Part A. Please simplify your results so that negation symbols appear directly in front of predicates, and not quantifiers or parenthetical expressions. So, an expression like -Vx: P(x) needs further simplification, as does By: (P(y) V Q(y)). Please show your steps. 7
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