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 english of. 3XVy[¬N(x) A W(x)]A[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 english of. 3XVy[¬N(x) A W(x)]A[R(y)→¬F(x,y)]

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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Question

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 english of.
3xVy[¬N(x)A W(x)] ^ [R(y) → ¬F(x,y)]

Expert Solution

Step 1

The symbolic is given as follows:

$\exists x \forall y [\neg N (x) \land W (x)] \land [R (y) \to \neg F (x, y)]$

We are given that:

$F (x, y) : " x is friends with y " N (x) : " x is funny " W (x) : " x is Wise " R (x) : " x is fair "$

We will break the given symbolic into two and then translate it into English.

$\exists x \forall y [\neg N (x) \land W (x)]$

This in English can be written as follows:

For some $x$ and all $y$ , $x$ is not funny but $x$ is wise.

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