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Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The domain for x and y is the set of all persons. Write the negation in English starting by "Some.. " of: Vx 3y w(x)-→R(y) ^ F(x,y)

Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The domain for x and y is the set of all persons. Write the negation in English starting by "Some.. " of: Vx 3y w(x)-→R(y) ^ F(x,y)

Advanced Engineering Mathematics
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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Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The domain for x and y is the set of all persons. Write the negation in English starting by "Some .. " of: Ey w(x)→R(y) A F(x,y)
Transcribed Image Text:Let F(x,y): "x is friend with y", N(x): "x is funny", W(x): "x is wise", R(x): "x is fair". The domain for x and y is the set of all persons. Write the negation in English starting by "Some .. " of: Ey w(x)→R(y) A F(x,y)
Expert Solution
Step 1

The symbolics given is as follows:

∀x∃y Wx→Ry∧Fx,y

We are also given:

Fx,y: "x is friends with y"Nx: "x is funny"Wx: "x is wise"Rx: "x is fair"

We are asked to write the negation of the above symbolics in english.

The negation of the given symbolics is as follows:

∃x∀y ¬Wx→¬Ry∧Fx,y∃x∀y ¬Wx→¬Ry∨¬Fx,y

Hence the symbolics that has to be translated to English is as follows:

∃x∀y ¬Wx→¬Ry∨¬Fx,y

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