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 |
⊤ or 1 |
-1 |
T, tautology |
false |
false |
False |
⊥ or 0 |
0 |
F, contradiction |
not P |
!p |
not p |
¬P or P |
~p |
|
P and Q |
p && q |
p and q |
P∧Q |
p & q |
PQ, P⋅Q |
P or Q |
p || q |
p or q |
P∨Q |
p | q |
P+Q |
P xor Q |
p != q |
p != q |
P⊕Q |
p ^ q |
P⊻Q |
P implies Q |
|
|
P→Q |
|
P⊃Q, P⇒Q |
P iff Q |
p == q |
p == q |
P↔Q |
|
P⇔Q, P xnor Q |
equivalent |
≡ |
A≡B means A↔B is a tautology |
entails |
⊨ |
A⊨B means A→B is a tautology |
provable |
⊢ |
A⊢B means A proves B ; it means both A⊨B and I know B is true because A is true
⊢B (i.e., without A) means I know B is true |
therefore |
∴ |
∴A means both the lines above this ⊢A
∴A also connotes A is the thing we wanted to show |