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1. Let B(r) denotes " plays this 2-person video game" and P(x, y) denotes "z has played this 2-person video game with y", where the domain for variables r and y consists of all students in your class. Questions: • Express each of the following sentences in logical notation. Define all set and predicate symbols that you use in the logical expressions. .Write the negation of each of the sentences in English and in logical form. Simplifying the logical sentences so that only predicates are negated. (a) If Aisha and Zulfiqar play this 2-person video game, then they have played it with each other. (Hint: note that P(x, y) only expresses that r has played with y; this does not necessarily mean that y has played with z). (b) No one in the class has played this 2-person video game with Jerry. (c) Someone in your class does not play this 2-person video game. (d) Everyone in your class who plays this 2-person video game has played the game with at least one

1. Let B(r) denotes " plays this 2-person video game" and P(x, y) denotes "z has played this 2-person video game with y", where the domain for variables r and y consists of all students in your class. Questions: • Express each of the following sentences in logical notation. Define all set and predicate symbols that you use in the logical expressions. .Write the negation of each of the sentences in English and in logical form. Simplifying the logical sentences so that only predicates are negated. (a) If Aisha and Zulfiqar play this 2-person video game, then they have played it with each other. (Hint: note that P(x, y) only expresses that r has played with y; this does not necessarily mean that y has played with z). (b) No one in the class has played this 2-person video game with Jerry. (c) Someone in your class does not play this 2-person video game. (d) Everyone in your class who plays this 2-person video game has played the game with at least one

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
Chapter4: Polynomials
Section4.1: Exponents
Problem 24OE
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Just complete questions a,b,c

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1. Let B(2) denotes "z plays this 2-person video game" and P(x, y) denotes "z has played this 2-person video game with y", where the domain for variables r and y consists of all students in your class. Questions: • Express each of the following sentences in logical notation. Define all set and predicate symbols that you use in the logical expressions. • Write the negation of each of the sentences in English and in logical form. Simplifying the logical sentences so that only predicates are negated. (a) If Aisha and Zulfiqar play this 2-person video game, then they have played it with each other. (Hint: note that P(r, y) only expresses that r has played with y; this does not necessarily mean that y has played with z). (b) No one in the class has played this 2-person video game with Jerry. (c) Someone in your class does not play this 2-person video game. (d) Everyone in your class who plays this 2-person video game has played the game with at least one other student in your class. (e) A student in your class has played this 2-person video game with everyone in your class.
Transcribed Image Text:1. Let B(2) denotes "z plays this 2-person video game" and P(x, y) denotes "z has played this 2-person video game with y", where the domain for variables r and y consists of all students in your class. Questions: • Express each of the following sentences in logical notation. Define all set and predicate symbols that you use in the logical expressions. • Write the negation of each of the sentences in English and in logical form. Simplifying the logical sentences so that only predicates are negated. (a) If Aisha and Zulfiqar play this 2-person video game, then they have played it with each other. (Hint: note that P(r, y) only expresses that r has played with y; this does not necessarily mean that y has played with z). (b) No one in the class has played this 2-person video game with Jerry. (c) Someone in your class does not play this 2-person video game. (d) Everyone in your class who plays this 2-person video game has played the game with at least one other student in your class. (e) A student in your class has played this 2-person video game with everyone in your class.
d) Logical expression of the given statement: Vx B(x) → y P(x,y). Set Symbols: None. Predicates: B(x), P(x,y). Negation of the statement: There is a student who plays this 2-person video game, had not played the game with Logical expression of the Negation statement: 3x B(x) → Vy(¬P(x,y)). e) Logical expression of the given statement: 3x B(x) → vy P(x,y). Set Symbols: None. anyone. Predicates: B(x), P(x,y). Negation Statement: For any student in the class has played this 2-person video game such that they are not played with anyone. Logical expression of the Negation statement: Vx B(x)→ 3y (¬P(x,y)).
Transcribed Image Text:d) Logical expression of the given statement: Vx B(x) → y P(x,y). Set Symbols: None. Predicates: B(x), P(x,y). Negation of the statement: There is a student who plays this 2-person video game, had not played the game with Logical expression of the Negation statement: 3x B(x) → Vy(¬P(x,y)). e) Logical expression of the given statement: 3x B(x) → vy P(x,y). Set Symbols: None. anyone. Predicates: B(x), P(x,y). Negation Statement: For any student in the class has played this 2-person video game such that they are not played with anyone. Logical expression of the Negation statement: Vx B(x)→ 3y (¬P(x,y)).
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