From English to Logic
Everyone can succeed, but Bob can't.
b: Bob
Sx: x can succeed
What is (∀x)(Sx) ∧ ~ Sb ?
~Gu ⟹ ~Ku
u : you
Kx : x knows
Gx : x goes
What is "You'll never know if you don't go? (or if you don't go, then you won't/don't know)
Bb.
∴ (∃x) Bx
b is a constant.
What is ~Bb using universal instantiation ?
A statement with a collection of premises and a conclusion in which it is not possible for all the premises to be true and the conclusion to be false.
What is a valid argument?
All that glitters is gold.
Lx : x glitters
Gx: x is gold
What is (∀x)(Lx ⟹ Gx) ?
(∃x)(Txm)
m: me
Txy: x once told y
What is "somebody once told me"?
Rab.
(∀x)(Rax ⟹ Rbx)
∴ Rbb
a,b are constants
What is "Rab ⟹ Rbb" using universal instantiation and ~Rab using the implication ?
This term, when paired with a matching predicate, leads to a proposition which is either true or false
What is a constant?
In the 1930s, this logician proved a famous collection of Incompleteness theorems which caused waves of doubt throughout the mathematical community.
Who is Kurt Gödel?
There are people who actually get out of bed when they turn off their alarm.
Bx: x actually gets out of bed
Ax: x turns off their alarm
What is (∃x)(Ax ⟹ Bx)?
(∀x) (Lxb ∧ ~Lbx)
b: Bob
Lxy: x loves y
What is "everyone loves bob, but Bob doesn't love them (back)"?
DAILY DOUBLE!!!!
What is (∀x)~(Px ∧ Qx), ~(Pa ∧ Qa), ~(Pb ∧ Qb) using negation of ∃, and universal instantiation twice?
This term, when paired with both a matching predicate and a quantifier (existential or universal), leads to a proposition which is either true or false.
What is a free variable?
Who is Bertrand Russell?
The enemy of my enemy is my friend.
m: me
Exy: x is the enemy of y
Fxy: x is the friend of y
What is (∀x)(∀y) (Exy ∧ Eym ⟹ Fxm) ?
(∀x) (((∃y)Mxy) ⟹ ~(∀y)(Mxy))
Mxy: x is married to y
What is "anyone who is married (to someone) cannot be married to everyone (at the same time)" ?
(or "for anyone who is married, it cannot be that they are married to everyone")
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What is:
4. ((∃y)Lay ⟹ (∀z) Lza) by UI
5. ((∃y)Lby ⟹ (∀z) Lzb) by UI
9. ~ (∃y)Lby , (∀z) Lzb by Implication
10. (∀y) ~Lby, Lab by negation of ∃ and UI
An adjective used to describe predicates which require two constants in order to form a proposition.
What is dyadic? (or a dyadic predicate)
When challenged to a pistol duel over a broken love affair, this French mathematician wrote down his ideas in a letter before being tragically wounded and dying at the age of 20. His work has become foundational to many branches of abstract algebra.
Who is Évariste Galois?
If Bob steals from a stealer, then Bob is not a stealer.
b: Bob
Sxy: x steals from y
(Note) A stealer is someone who steals from somebody.
What is (∃x)(Sbx ∧ ((∃y)Sxy)) ⟹ ~(∃y)(Sby) ?
What is "all love all lovers" or "Everyone loves every lover" ?
See image for this question
See answer image for this question
What is a complete system (of natural deductions)?
This female French mathematician proved many results ranging from abstract algebra to her theorem in theoretical physics on the connection between symmetries of a system and conservation laws.
Who is Emily Noether?