2. Examples in Plain English
1.
2.
3.
4.
5.
It rains because we prayed
causation,
correlation...
It rains after we prayed
We go to school unless it rains
If we go to school, it rains
We don’t go to school only if it rains
Any logic in these sentences?
How about truth tables?
Some of the sentences are not
truth-functional
7. Biconditional Symbol ↔
●
●
●
●
A
A
A
A
↔B
if and only if B
iff B
“just in case” B (in math only)
○ Math: n is even just in case n2 is even
○ Real life: We took umbrellas just in case it
rains
10. Completeness
Given a truth-valued function, can it be
expressed via the connectives we know?
E.g. via ∧v¬?
Easy for n=1:
P
f1
f2
f3
f4
T
T
T
F
F
F
T
F
T
F
General case? f(P1, P2, …, Pn)
12. Peirce’s Arrow
NOR, aka ↓
A ↓ B ⇔ ¬(AvB)
¬A ⇔ A↓A
AvB ⇔ ¬¬(AvB) ⇔ ¬(A↓B) ⇔ (A↓B)↓(A↓B)
“A or B” is “neither (neither A or B) nor (neither A or B)
Other solutions?