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Tulane - MATH 1210 - Class Notes - Week 1

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≡ ⊃ v • ~

A ≡ B/(A ⊃ B) • (B ⊃ A)

T T T T T T T T T T

T F F T F F F F T T Don't forget about the age old question of What makes an acid an acid?

F F T F T T F T F F ← most obvious exampleIf you want to learn more check out What is illegal home brew made by adding sugar to accelerate corn fermentation?

F T F F T F T F T F

Reducing and conjuncting

A ≡ B logically equivalent can always beDon't forget about the age old question of State the difference between generalization and discrimination.

A if and only B substituted with something that hat If you want to learn more check out Who was the first researcher to really focus on bureaucracy?

If ⇒ ⊃ the same truth value without

Only if ⇒ ⊃ changing the meaning.If you want to learn more check out the fact that the words “whiskey makes you sick when you’re well,” when arranged differently, “whiskey, when you’re sick, makes you well,” create a totally different meaning is related to which rule of language?

↓

B ⊃ A A ⊃ BIf you want to learn more check out rate my professor ecu

→ we have now basically eliminated the need for ≡, the next easiest one to “get rid of” is ⊃.

x ≡ y → (x ⊃ y) • (y ⊃ x) → ~ (x • ~y) • ~(y • ~x)

G V H ⎫

T T T → G • H ⎪

T T F → G • ~H False: ~(~G • ~H) ⎪

F T T → ~G • H ⎪

F F F ⎪

~G • ~H ⇒ V ⇒ False ⎬in order to get rid of both

~ (~ G • ~ H) ⎪these a new operator needs

T F T F F T Truth table proving the above. ⎪to be introduced. Why?

T F T F T F ⎪ - for computing (new computer

T T F F F T ⎪process). Will not be tested

F T F T T F ⎭on why.

One operator : A • B ~ x → one operator that definition

says ~(x • y) / (x | y) I = Pike

F T T T T F T X I Y

T T F F T T F T F T

T F F T F T T I=Nand not and T F F

T F F F F T F when translated F T T

into english F T F

(no real translation) reverses truth table

Ex. ~ A / A I A

F T T F T

T F F T F

Ex. A • B / (A I B) I (A I B)

T T T T F T T T F T

T F F T T F F T T F

F F T F T T F F T T

F F F F T F F F T F

Pikes makes all other operators ≡̷ ̷⊃̷ ̷v̷ ̷•̷ ̷~̷ unnecessary

~[~(A • B) • ~(A • B)]

HW: 1 0 0 1

0 1 0 1 ~ (A ≡ B)

1 1 0 0