(LOGIC) Construct a truth table to show that the preposition (~P v ~Q) ⇒ (P ^ ~Q) ALWAYS takes the value of p?
⇒ means A ⇒ B means if A is true then B is also true; if A is false then nothing is said about B.
~ means The statement ~A is true if and only if A is false.
^ means The statement A ^ B is true if A and B are both true; else it is false.
v means The statement A v B is true if A or B (or both) are true; if both are false, the statement is false.
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Verified answer
P ... Q .... ( ~ P v ~ Q ) ... (P ^ ~ Q) ... a → b
. . . . . . . . . . . . a . . . . . . . . b
T ... T . . . . . . . . F . . . . . . . . F . . . . . . T
T ... F . . . . . . . . T . . . . . . . . T . . . . . . T
F ... T . . . . . . . . T . . . . . . . . F . . . . . . F
F ... F . . . . . . . . T . . . . . . . . F . . . . . . F
Since last column matches first column, we have shown the equivalence.