Logic and FOL Assignment 4: Formal Logic - University PHIL 279

This document presents the solutions to Logic and First-Order Logic (FOL) Assignment 4, likely part of a university-level philosophy course (PHIL 279). The assignment involves translating sentences into FOL using provided symbolization keys, creating symbolization keys for given sentences, and determining whether given expressions are sentences or formulas in FOL. The solutions cover a range of logic concepts, including quantifiers, predicates, and logical connectives. The assignment also assesses the ability to represent complex relationships and statements using formal logic notation.

Running head: LOGIC ASSIGNMENT 4
Logic and FOL Assignment 4
Name of the Student
Name of the University
Author note

1LOGIC ASSIGNMENT 4
Ǝ →↔˄˅Ɐ ¬
Q1.
a) Ɐx(Mx=Sx)
b) [Ɐx Ɐy (Cx˄¬Cy)] →Bxy
c) [Ɐx(Cx˄¬Sx)] →(¬Tbx˄Tcx)
d) [Ɐx(Cx˅Mx)] ↔Tbx
e) [Ɐx(Cx˅Mx)] →( Tbx˄Tcx)
f) [ƎxƎy(¬x=y˄¬Sx˄Cx˄¬Sy˄Cy) ˄ Ɐz(Cz˄Mz)] →(Tzx˄Tzy)
g) ƎxƎyƎz(¬x=y˄¬y=z˄Cx˄Cy˄Cy˄Sx˄Sy˄Sy) ↔(Tcx˄Tcy˄Tcz)
Q2.
Symbolisation Key
Rxy: x and y are relatives
Fx: x is female
M: x is male
Sxy: x and y are siblings
Txy: x is taller than y
Ax: x is athletic
Uxy: x is uncle or aunt of y
Doha: d
Tim: t
a) Ɐx[ƎyƎz(¬y=z˄Rxy˄Rxz)

2LOGIC ASSIGNMENT 4
b) Ɐx[(x=¬d) →Ttx]
c) ⱯxⱯyⱯz[(Uxd˄Uyd˄Uzd˄Uxd˄Uyd˄Uzd)→(x=y˅y=z˅x=z)]
d) Ɐx (Ad˄Rdx˄Ax)
e) ((At˄ Sxt˄Mx) →Ax)˄(ƎyƎzƎw[(y=¬z˄z=¬w˄y=¬w˄Syt˄My˄Sz˄Mz˄Sw˄Mw)
→(Tyt˄Tzt˄Twt)]
f) (Sdt˄Fd) ↔Rdt
g) (ƎyƎzƎw[(y=¬z˄z=¬w˄y=¬w˄Uyd˄Fy˄Uzd˄Fz˄Uwd˄Fw˄Tyd˄Tzd˄Twd)])˄(Ǝx(Rxd
˄ x=¬y˄x=¬z˄x=¬w))
3. The two place predicate R is a Symbolisation of a definite sentence that implies that only x
can be comprised in both of the place of R where y and w can have those place alternatively
if x is present with w and which is true for all means of x.
4.
a) The given expression is a sentence of FOL
There is no conditional phrase that exist out of the declaration of existence of both w and x.
b) The given expression is a sentence of FOL
There is no conditional phrase that exist out of the declaration of existence of both z and v.
c) The given expression is a sentence of FOL
There is no conditional phrase that exist within the expression.
d) The given expression is a sentence of FOL
There is no conditional phrase that exist out of the declaration of existence of both x and y.
e) The given expression is a Formula

3LOGIC ASSIGNMENT 4
There is a clear independent relationship between the existence of x and the predicate F
f) The given expression is a sentence of FOL
There is no conditional phrase that exist within the expression.
g) The given expression is a Formula
There is a clear independent relationship between the existence of x, y and z and the 4 place
predicate F
h) The given expression is a Formula
There is a clear independent relationship between the existence of x and y and the predicate T

4LOGIC ASSIGNMENT 4
Bibliography:
Magnus, P.D., 2005. forall x: An introduction to formal logic.