Write down the truth table for the compound proposition(p -> q) ->((p V r ) ->(q Vr )) :Is this a tautology, a contradiction or neither?
What have you done on this? Do you see that there will be 8 "cases", 8 rows in your truth table? How many columns there are depends upon how you want it "divided". Personally, I would start with three columns for the various values of r, s, and t, then a column for p-> q, a column for (p v r), a column for (q v r), a column for (p v r)-> (q v r), and finally, a column for the entire statement.
Now, do you know what a "tautology" and a "contradiction" are?
My answer
p. q. r........ (p->q)... (p v r) ...(q v r ) ...(p v r )->(q v r ) ...(p->q)->((p v q)->(q v r) )
F.F.F...............T........... F.......... F.................... T............................. T
F .F.T.............. T.......... T ..........T ...................T.............................. T
F. T. F ..............T .........F ......... T................... T ...............................T
F .T. T.............. T .........T ...........T.................. T ...............................T
T. F. F.............. F......... T............ F................. F ................................T
T. F .T.............. F .........T ...........T................. T................................. T
T. T. F.............. T ........T ............T................. T ................................T
T. T. T............... T........T............. T................ T..................................T
.
I'm guessing it's Tautology because the whole statement is true regardless of the value of the individual statements.
Contradiction means it would contradict and be opposites of the truth values ..(I just put dots in to separate the truth values )
Hmm Is my answer ok ?...thanks
G'day Plato chuck another shrimp on the barbie
ok it's Tautology as the results are all True.
Thanks Plato . Yes I just saw your post as I was putting in the table separating it with dots ...
Thanks for the tool that helps with Truth tables