Home > College Algebra calculators > Mathematical Logic, truth tables, logical equivalence calculator

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
Problem: logical validity Hypothesis = p=>q,p=>r and Conclusion = p=>(q and r) [ Calculator, Method and examples ]

Solution:
Your problem `->` logical validity Hypothesis = p=>q,p=>r and Conclusion = p=>(q and r)


Hypothesis :
`S_1:p=>q`

`S_2:p=>r`

Conclusion :
`S : p=>(q^^r)`


`(1)``(2)``(3)``(4)=(1)=>(2)``(5)=(1)=>(3)``(6)=(2)^^(3)``(7)=(1)=>(6)`
`p``q``r``S_1`
`p=>q`
`S_2`
`p=>r`
`q^^r``S`
`p=>(q^^r)`
TTTTTTcritical rowT
TTFTFFF
TFTFTFF
TFFFFFF
FTTTTTcritical rowT
FTFTTFcritical rowT
FFTTTFcritical rowT
FFFTTFcritical rowT


The conclusion `(S)` is true in all critical rows. So the argument is logically valid.








Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me
  
 

 
Copyright © 2019. All rights reserved. Terms, Privacy





We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more