Let P denote the proposition “The moon is made of cheese”
Let Q denote the proposition “The moon is red”
The sentence “If the moon is red, it is not made of cheese” is translated as propositional formula Q ⊃ (¬P)
P |
Q |
P ∧ Q |
false |
false |
false |
false |
true | false |
true | false | false |
true |
true |
true |
true iff (if and only if) both operands are true
P |
Q |
P ∨ Q |
false |
false |
false |
false |
true | true |
true | false | true |
true |
true |
true |
true iff (if and only if) either operands are true
P |
¬P |
false |
true |
true | false |
P |
Q |
P ⊃ Q |
false |
false |
true |
false |
true | true |
true | false | false |
true |
true |
true |
true iff first is true and second is true or the first is false.
P |
Q |
P ≡ Q |
false |
false |
true |
false |
true | false |
true | false | false |
true |
true |
true |
true iff both operands have the same value.
P |
Q |
¬P |
(¬P) ⊃Q |
P ∧((¬P) ⊃Q) |
false | false | |||
false | true | |||
true | false | |||
true |
true |
|||
The values in the last column determine the value of the proposition: