Q: Is this truth or false An irrational number cannot be a real number?

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A truth table is a chart of all of the possible combinations of true and false for a given set of options. The first step is to make x number of columns, where x is the number of inputs there are. Then in the first column write down x trues, followed by x false. Then in the following columns write down x/2 trues and false, alternating then x/4, then x/8 and so on.

The graphics facilities available in this browser do not lend themselves to creating truth tables. Hope the following survives the browser (ignore the dots: they are needed for spacing)...............| Y True | Y False|X True...| True ...| False...|X False. | False...| False...|

"P and not P" is always false. If P is true, not P is false; if P is false, not P is true. In either case, combining a true and a false with the AND operator gives you false. And if you look at the truth table for the implication (the "therefore" part), when the left part is false, the result is always true.

The graphics facilities available in this browser do not lend themselves to creating truth tables. Hope the following survives the browser (ignore the dots: they are needed for spacing)...............| Y True | Y False|X True...| True ...| True ...|X False. | True ...| False...|

If p is true and q is false, p or q would be true. I had a hard time with this too but truth tables help. When using P V Q aka p or q, all you need is for one of the answers to be true. Since p is true P V Q would also be true:)

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A truth table is a chart of all of the possible combinations of true and false for a given set of options. The first step is to make x number of columns, where x is the number of inputs there are. Then in the first column write down x trues, followed by x false. Then in the following columns write down x/2 trues and false, alternating then x/4, then x/8 and so on.

The graphics facilities available in this browser do not lend themselves to creating truth tables. Hope the following survives the browser (ignore the dots: they are needed for spacing)...............| Y True | Y False|X True...| True ...| False...|X False. | False...| False...|

Assuming that you mean not (p or q) if and only if P ~(PVQ)--> P so now construct a truth table, (just place it vertical since i cannot place it vertical through here.) P True True False False Q True False True False (PVQ) True True True False ~(PVQ) False False False True ~(PVQ)-->P True True True False if it's ~(P^Q) -->P then it's, P True True False False Q True False True False (P^Q) True False False False ~(P^Q) False True True True ~(P^Q)-->P True True False False

The graphics facilities available in this browser do not lend themselves to creating truth tables. Hope the following survives the browser (ignore the dots: they are needed for spacing)...............| Y True | Y False|X True...| True ...| False...|X False. | False...| False...|

This is true. Plato believed souls could not fully understand truth and therefore, cannot understand the Forms.