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The concept of satisfiable is mentioned above. Compared to the other answers given, the truth table seems to make the most sense from my perspective. I will ask for clarity on the "satisfiable" concept. Thanks!

Hello, I am confused on much of the following... Determine if the following formulas are satisfiable. P' is the negation of P. (P→Q)→(Q'→P') <-- I read this as being P=true then Q=true, Q'=false then P'=false, so Q=true implies Q'=false??? (Q→R)→((P→Q)→(P→R)) <-- I read this as (Q→R)→(Q→R)...

I need to prove (without plugging numbers in) that the equation holds true for the range of p specified.

I should have mentioned this is from a probability example so the value that p can take on is between 0 and 1. So basically between 0 as a lower limit and less than 0.5 for the upper limit is should hold true. Unfortunatly plugging in number doesnt act as a proof :(

x = 3p^2 − 2p^3 Show that x < p iff p < 1/2 note: p^2 = p'squared and p^3 = p'qubed Thanks!