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4. Write the following statements in plain English. It is not sufficient to literally translate every symbol; make the result a sentence a human would say. (a) VxEU, 3y ES, F(x, y). (b) 3x EU, VyET, F(x, y). 1 (c) VxES, Vye S, 3z EU, (F(x,z) ^ F(y,z)). (d) VxU,(3y € T,F(x, y)) ⇒ (VyɛT,F(x, y)).

4. Write the following statements in plain English. It is not sufficient to literally translate every symbol; make the result a sentence a human would say. (a) VxEU, 3y ES, F(x, y). (b) 3x EU, VyET, F(x, y). 1 (c) VxES, Vye S, 3z EU, (F(x,z) ^ F(y,z)). (d) VxU,(3y € T,F(x, y)) ⇒ (VyɛT,F(x, y)).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.4: Binary Operations
Problem 14E: Assume that is a binary operation on a non empty set A, and suppose that is both commutative and...
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In this section, U will denote the universal set: the set of students at some university. S will denote the set of students on the soccer team, T will denote the set of students on the tennis team, and F(x, y) will denote the open sentence "x is friends with y". 3. Write the following statements using quantifier notation and logical operations. (a) Two people on the same team are always friends. (b) Nobody on the soccer team is friends with anyone on the tennis team. (c) A student who is friends with someone on the soccer team is also friends with someone on the tennis team. (d) Any two tennis players have a common friend on the soccer team. Note on commas: in symbolic form, these only belong after a quantified variable, such as when writing "VxEU,...". Do not use them between two substatements: if you're tempted to write "P,Q" then you probably mean either "PAQ" or "P⇒Q". 4. Write the following statements in plain English. It is not sufficient to literally translate every symbol; make the result a sentence a human would say. (a) VxEU, 3y ES, F(x, y). (b) 3x EU, VyET, F(x, y). 1 (c) VxES, VуES, 3z EU, (F(x,z)^F(y,z)). (d) VxEU,(3y ET, F(x, y)) (VyT, F(x, y)).
Transcribed Image Text:In this section, U will denote the universal set: the set of students at some university. S will denote the set of students on the soccer team, T will denote the set of students on the tennis team, and F(x, y) will denote the open sentence "x is friends with y". 3. Write the following statements using quantifier notation and logical operations. (a) Two people on the same team are always friends. (b) Nobody on the soccer team is friends with anyone on the tennis team. (c) A student who is friends with someone on the soccer team is also friends with someone on the tennis team. (d) Any two tennis players have a common friend on the soccer team. Note on commas: in symbolic form, these only belong after a quantified variable, such as when writing "VxEU,...". Do not use them between two substatements: if you're tempted to write "P,Q" then you probably mean either "PAQ" or "P⇒Q". 4. Write the following statements in plain English. It is not sufficient to literally translate every symbol; make the result a sentence a human would say. (a) VxEU, 3y ES, F(x, y). (b) 3x EU, VyET, F(x, y). 1 (c) VxES, VуES, 3z EU, (F(x,z)^F(y,z)). (d) VxEU,(3y ET, F(x, y)) (VyT, F(x, y)).
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