Define the following predicates on the domain of all people. 5(x): "x is a student." T(x):"x is a teacher." F(x,y):"x and y are distinct people who are friends with one another." (You can assume the F predicate is symmetric so that F(x,y) and F(y,x) are equivalent.) a. Consider the statements Vx3y[S(x) → F(x,y)] and 3yVx[S(x)→F(x,y)]. Express each statement verbally and explain how they differ in meaning. b. Express the statement symbolically. "Teachers are never friends with students."
Define the following predicates on the domain of all people. 5(x): "x is a student." T(x):"x is a teacher." F(x,y):"x and y are distinct people who are friends with one another." (You can assume the F predicate is symmetric so that F(x,y) and F(y,x) are equivalent.) a. Consider the statements Vx3y[S(x) → F(x,y)] and 3yVx[S(x)→F(x,y)]. Express each statement verbally and explain how they differ in meaning. b. Express the statement symbolically. "Teachers are never friends with students."
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![Define the following predicates on the domain of all people.
S(x): "x is a student."
T(x): "xis a teacher."
F(x,y): "x and y are distinct people who are friends with one another."
(You can assume the F predicate is symmetric so that F(x,y) and F(y,x) are equivalent.)
a. Consider the statements Vx3y[S(x) → F(x,y)] and 3yVx[S(x)→F(x, y)]. Express each
statement verbally and explain how they differ in meaning.
b. Express the statement symbolically. "Teachers are never friends with students."](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe4606c36-830f-4cc8-9c7f-4ce72d7d3a5a%2Fe443ae1a-cd78-4fcb-8dad-684ae6ec7605%2F02ovhdn_processed.png&w=3840&q=75)
Transcribed Image Text:Define the following predicates on the domain of all people.
S(x): "x is a student."
T(x): "xis a teacher."
F(x,y): "x and y are distinct people who are friends with one another."
(You can assume the F predicate is symmetric so that F(x,y) and F(y,x) are equivalent.)
a. Consider the statements Vx3y[S(x) → F(x,y)] and 3yVx[S(x)→F(x, y)]. Express each
statement verbally and explain how they differ in meaning.
b. Express the statement symbolically. "Teachers are never friends with students."
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