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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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