Truth tables for these calculus formulae

  • Thread starter Thread starter charmedbeauty
  • Start date Start date
  • Tags Tags
    Calculus Formulae
Click For Summary
SUMMARY

The discussion focuses on constructing truth tables for the propositional calculus formulae (p→(~q)) ∧ r and q→((~p) ∧ r). The user presents their truth tables and requests verification of their solutions against provided answers. The truth tables include combinations of truth values for variables p, q, and r, yielding results for the expressions. The user expresses uncertainty about the correctness of their tables, which display logical outcomes based on the given formulae.

PREREQUISITES
  • Understanding of propositional calculus
  • Familiarity with logical operators such as implication (→) and conjunction (∧)
  • Ability to construct and interpret truth tables
  • Basic knowledge of logical negation (~)
NEXT STEPS
  • Study the principles of propositional logic
  • Learn how to construct truth tables for more complex logical expressions
  • Explore logical equivalences and their applications in propositional calculus
  • Practice solving problems involving logical operators and truth values
USEFUL FOR

Students studying logic, mathematics, or computer science, particularly those working on propositional calculus and truth table construction.

charmedbeauty
Messages
266
Reaction score
0

Homework Statement



Construct truth tables for the two propositional calculus formulae

(p→(~q))\wedger and q→((~p)\wedger)

Homework Equations


The Attempt at a Solution



Can some one please check these solutions because I had a look at the answer and it was different but I don't think I am wrong.

Sorry about the layout I tried pasting of a word doc table but did not work out to well.

Just follow the vales with each column respectively.
Code: 
p   ,	q  ,	r  ,	(p(~q)) [itex]\wedge[/itex] r  ,  ((~p) [itex]\wedge[/itex] r)

T	T	T	    F	                     F
T	T	F	    F	                     F
T	F	T	    T	                     T
T	F	F	    F	                     T
F	T	T	    T	                     T
F	T	F	    F	                     F
F	F	T	    T	                     T
F	F	F	    F	                     T
Is this right??
 
Last edited:
Physics news on Phys.org
charmedbeauty said:

Homework Statement



Construct truth tables for the two propositional calculus formulae

(p→(~q))\wedger and q→((~p)\wedge

Homework Equations



The Attempt at a Solution



Can some one please check these solutions because I had a look at the answer and it was different but I don't think I am wrong.

Sorry about the layout I tried pasting of a word doc table but did not work out to well.

Just follow the vales with each column respectively.

p , q , r , (p→(~q)) \wedge r , (q→(~p) \wedge r)

T T T F F
T T F F F
T F T T T
T F F F T
F T T T T
F T F F F
F F T T T
F F F F T

Is this right??
To get better spacing use the [code ] tag.

Code: 
p   ,	q  ,	r  ,	(p→(~q)) ∧ r  ,  (q→(~p) ∧ r)

T	T	T	    F	                     F
T	T	F	    F	                     F
T	F	T	    T	                     T
T	F	F	    F	                     T
F	T	T	    T	                     T
F	T	F	    F	                     F
F	F	T	    T	                     T
F	F	F	    F	                     T
 
Last edited:
SammyS said:
To get better spacing use the [code ] tag.

Code: 
p   ,	q  ,	r  ,	(p(~q)) ∧ r  ,  ((~p) ∧ r)

T	T	T	    F	                     F
T	T	F	    F	                     F
T	F	T	    T	                     T
T	F	F	    F	                     T
F	T	T	    T	                     T
F	T	F	    F	                     F
F	F	T	    T	                     T
F	F	F	    F	                     T

Ok thanks but is it right?
 

Similar threads

Avoid unpleasant integrals in solving IVP
  • · Replies 3 ·
Replies
3
Views
2K
[LinAlg] Set Notation, Subspaces, Bases, Ranges, & Kernels
  • · Replies 9 ·
Replies
9
Views
2K
Question about Finding a Force with line integrals
  • · Replies 20 ·
Replies
20
Views
3K
Trying to reconcile function composition problems with sets & formulas
  • · Replies 3 ·
Replies
3
Views
1K
Work done by Three Dimensional Inverse Square Field
  • · Replies 3 ·
Replies
3
Views
2K
Find the Surface integral of a Paraboloid using Stoke's Theorem
  • · Replies 4 ·
Replies
4
Views
2K
How Do Matrix ODEs Relate to Determinants and Traces?
  • · Replies 3 ·
Replies
3
Views
2K
Line integral of vector field from Apostol calculus
  • · Replies 3 ·
Replies
3
Views
2K
2nd order differential equation (nonhomogenous)
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Correct Upper/Lower limits for continuation of solutions for ODE
  • · Replies 0 ·
Replies
0
Views
4K