You have enough to worry about memorizing without keeping dozens of symbols in your head at once. We intend to provide this table for your reference during every in-class evaluation.
| true |
true |
True |
\top or 1 |
-1 |
T, tautology |
| false |
false |
False |
\bot or 0 |
0 |
F, contradiction |
| not P |
!p |
not p |
\lnot P or \overline{P} |
~p |
|
| P and Q |
p && q |
p and q |
P \land Q |
p & q |
P Q, P \cdot Q |
| P or Q |
p || q |
p or q |
P \lor Q |
p | q |
P + Q |
| P xor Q |
p != q |
p != q |
P \oplus Q |
p ^ q |
P ⊻ Q |
| P implies Q |
|
|
P \rightarrow Q |
|
P \supset Q, P \Rightarrow Q |
| P iff Q |
p == q |
p == q |
P \leftrightarrow Q |
|
P \Leftrightarrow Q, P xnor Q |
| equivalent |
\equiv |
A \equiv B means A \leftrightarrow B is a tautology |
| entails |
\vDash |
A \vDash B means A \rightarrow B is a tautology |
| provable |
\vdash |
A \vdash B means A proves B ; it means both A \vDash B and I know B is true because A is true
\vdash B (i.e., without A) means I know B is true |
| therefore |
\therefore |
\therefore A means both the lines above this \vdash A
\therefore A also connotes A is the thing we wanted to show |