Use a truth table:
Under P put TTFF
Under Q put TFTF
x ⊃ y is usually true, and is only false in the one case "T ⊃ F", otherwise it's true.
x & y is usually false, and is only true in one case "T & T", otherwise it's false.
x v y is usually true, and is only false in one case "F v F", otherwise it's true.
P | Q | P ⊃ Q | (P ⊃ Q) & P | [(P ⊃ Q) & P] ⊃ Q |
T | T | T | T | T |
T | F | F | F | T |
F | T | T | F | T |
F | F | T | F | T |
Since there are all T's in the last column, the statement is called a "tautology". It's always true.
Edwin
