p q ~p ~q q⋀~p T T F F ? T F F T ? F T T F ? F F T T ? You need to learn the rules for the four basic symbols ⋀, ⋁, ->, and <-> Rules: ⋀ is T only for T⋀T, otherwise it's F. ⋁ is F only for F⋁F, otherwise it's T. -> is F only for T->F, otherwise it's T. <-> is T for T<->T, F<->F. <-> is F for T<->F, F<->T. You only have ⋀ here to do, but you need to learn those other three rules as well for other truth tables. Here goes: p q ~p ~q q⋀~p T T F F ? T F F T ? F T T F ? F F T T ? Let's look at q⋀~p. Let's do the top line: On the left of the ⋀ in q⋀~p is q, and on the top line q has T under it. On the right of the ⋀ in q⋀~p is ~p, and on the top line ~p has F under it. So on the top line q⋀~p is a case of T⋀F. So we look at the rule for ⋀, which is: "⋀ is T only for T⋀T, otherwise it's F." T⋀F is not a case of T⋀T, and therefore it's F. So we put an F on the top row underneath q⋀~p. So we now have this: p q ~p ~q q⋀~p T T F F F T F F T ? F T T F ? F F T T ? -------------------------------------------------------------- Next let's do the second line: On the left of the ⋀ in q⋀~p is q, and on the 2nd line q has F under it. On the right of the ⋀ in q⋀~p is ~p, and on the 2nd line ~p has F under it. So on the 2nd line q⋀~p is a case of F⋀F. So we look at the rule for ⋀, which is: "⋀ is T only for T⋀T, otherwise it's F." F⋀F is not a case of T⋀T, and therefore it's F. So we put an F on the 2nd line underneath q⋀~p. So we now have this: p q ~p ~q q⋀~p T T F F F T F F T F F T T F ? F F T T ? -------------------------------------------------------------- Next let's do the third line: On the left of the ⋀ in q⋀~p is q, and on the 3rd line q has T under it. On the right of the ⋀ in q⋀~p is ~p, and on the 3rd line ~p has T under it. So on the 3rd line q⋀~p is a case of T⋀T. So we look at the rule for ⋀, which is: "⋀ is T only for T⋀T, otherwise it's F." T⋀T is INDEED a case of T⋀T, and therefore it's T. So we put a T on the 3rd row underneath q⋀~p. So we now have this: p q ~p ~q q⋀~p T T F F F T F F T F F T T F T F F T T ? -------------------------------------------------------------- Next let's do the bottom line: On the left of the ⋀ in q⋀~p is q, and on the bottom line q has F under it. On the right of the ⋀ in q⋀~p is ~p, and on the bottom line ~p has T under it. So on the bottom line q⋀~p is a case of F⋀T. So we look at the rule for ⋀, which is: "⋀ is T only for T⋀T, otherwise it's F." F⋀T is not a case of T⋀T, and therefore it's F. So we put an F on the 2nd row underneath q⋀~p. So finally we have this: p q ~p ~q q⋀~p T T F F F T F F T F F T T F T F F T T F Do you now see how truth tables are done? You have to learn the rules for all four symbols ⋀, ⋁, ->, and <-> to do truth tables. Edwin