Conditionally so if not True or False
If it is pie or quiche, then it might be pie but not quiche, and it might be quiche but not pie, and it might be both pie and quiche, but it isn’t neither pie nor quiche.
It is pie.
Therefore:
It is pie or quiche.
If it is probable or questionable, then it might be probable but not questionable, and it might be questionable but not probable, and it might be both probable and questionable, but it isn’t neither probable nor questionable.
It is probable.
Therefore:
It is probable or questionable.
(P V Q) → ((P & Q) V (Q & P) V (P & Q)), ((P) & (Q))
P
├ P V Q
Introducing the Connectives
Argument Indicator
‘├’ Therefore
P├ P
The Disjunctive
‘V’ …Or…
P├ P V Q
The Conditional
‘→’ If…then…
P → (P & Q)├ P → Q
The Conjunctive
‘&’ …And…
P, Q├ P & Q
The Negation
‘‘ Not…
P → Q, Q├ P
Characters of the Connectives
Negation
P is false wherever P is true.
 P
F T
T F
If it isn’t probable, it is false to say that it is probable, and if it is probable, it’s false to say that it isn’t probable.
Conjunctive
P & Q is true only if P and Q are true.
P & Q
T T T
T F F
F F T
F F F
If it is probable and questionable it can’t be neither, nor can it be one but not the other, it has to be both.
Conditional
P → Q is true except if P is true and Q is false.
P → Q
T T T
T F F
F T T
F T F
If probability implies questionability, you cannot say it is true that it is probable whilst maintaining it is false to call it questionable.
Disjunctive
P V Q is true if P, or Q, or both P and Q are true, and not true if P and Q are both false.
P V Q
T T T
T T F
F T T
F F F
If it is pie or quiche, then it might be pie but not quiche, and it might be quiche but not pie, and it might be both pie and quiche, but it isn’t neither pie nor quiche.
It is pie.
Therefore:
It is pie or quiche.
