Question

Explain, without using a truth table, why (p ∨¬q) ∧
(q ∨¬r) ∧ (r ∨¬p) is true when p, q, and r have the
same truth value and it is false otherwise.

Answer 1

Hey :)
\(\Large\rm (p\vee\neg q)\wedge(q\vee\wedge r)\wedge(r\vee \neg p)\)

Grr I couldn't remember the symbols... took a while to find them lol
Hmmm what can we do...

Answer 2

Ahh I scrwed one up :c grr

Answer 3

Oh we can't use a truth table for this?
Hmm

Answer 4

p, q, r have the same truth value means they are all true or all false
1) They are all true
p is true
~q is false
the first part is (true or not false )= true
the middle one is (true or not false = true (again)
the last part is (true or not false) = true (again)
now combine them all, true "and" true "and" true = big True, right??
The same logic with all false. :)