Logic Week One And Two

Front 1

UNLESS means...

Back 1

if not

Front 2

‘P unless Q’

Back 2

~Q → P

Front 3

not P unless Q

Back 3

~Q → ~P

Front 4

You will not graduate unless you pass logic

Back 4

G = you will graduate
L = you pass logic

So, we want to figure out how to translate this:
not G unless L
• We saw that this can be understood as:
If not L, then not G
• Translating fully, we get:
~L → ~G

Front 5

If A, then B
A if B
A only if B
A unless B

Back 5

A → B
B → A
~B → ~A
~B → A

Front 6

Example (i): If neither Jay nor Kay is working, then we will go on vacation

Back 6

J = Jay is working
K = Kay is working
W = we go on vacation

‣ If neither Jay nor Kay is working, then we will go on vacation
‣ If (neither Jay is working nor Kay is working), then we go on vacation
‣ If (neither J nor K), then W
‣ If ~(J v K), then W
‣ ~(J v K) → W

Front 7

Example (ii): You will pass unless you goof off, provided that you are attentive

Back 7

P = You will pass
G = You goof off
A = you are attentive

You will pass unless you goof off, provided that you are attentive
‣ (You will pass unless you goof off), provided that you are attentive
‣ (P unless G), provided that A
‣ (~G → P), provided that A
‣ A → (~G → P)

Front 8

If Sam didn’t go to the shops then we have
nothing to eat nor drink. He didn’t go to the
shops. So we have nothing to eat nor drink.

Back 8

S = Sam went to the shops
E = We have something to eat
D = We have something to drink
~S → (~E & ~D)
~S
/ ~E & ~D