Flashcards
Logic Examples
Cards in this deck (66)
- 1If A U B = B, then B ⊂ AFalse
- 2If A U B = B, then A ⊂ BTrue
- 3If A ⊂ B, then A U B = BTrue
- 4If A ⊂ B, then A U B = AFalse
- 5A ∩ A = ATrue
- 6A ∩ B = B U AFalse
- 7A ∩ (B ∩ C) = (A ∩ B) ∩ CTrue
- 8A ∩ 0 = 0True
- 9If A ∩ B = B, then B ⊂ ATrue
- 10If A ∩ B = B, then A ⊂ BFalse
- 11If A ⊂ B, then A ∩ B = BFalse
- 12If A ⊂ B, then A ∩ B = ATrue
- 13If A ⊂ B, then A' ⊂ B'False
- 14If A ⊂ B, then B' ⊂ A'True
- 15Write truth tables for De Morgan's laws and express them as Venn diagramsCheck Tutorial 2
- 16- (P ʌ Q) ↔ (-P ʌ -Q)T2
- 17P ↔ -PT2
- 18P → -Q; -Q → R; P ⊢ R1. P → ¬Q A
2. ¬Q → R A
3. P A
4. ¬Q 1,3 MPP
5. R 2,4 MPP - 19P → (Q → R); P; -R ⊢ Q1. P → (Q → R) A
2. P A
3. ¬R A
4. Q → R 1, 2 MPP
5. ¬Q 3,4 MTT - 20P → -P ⊢ -P1. P → ¬P A
2. P A
3. ¬P 1, 2 MPP
4. P ∧ ¬P 2, 3 ∧I
5. ¬ P 2,4 RAA - 21P → Q; P → -Q ⊢ -P1. P → Q A
2. P → ¬Q A
3. P A
4. Q 1,3 MPP
5. ¬Q 2,3 MPP
6. Q ∧ ¬Q 4,5 ∧I
7. ¬P 3,6 RAA - 22P ʌ Q ⊢ Q ʌ P1. P ∧ Q A
2. P &E
3. Q &E
4.Q∧P 3,2&I - 23Q → R ⊢ (P ʌ Q) → (P ʌ R)1. Q → R A
2. P ∧ Q A
3.P 2 &E
4.Q 2 &E
5.R 1, 4 MPP
6. P ∧ R 3,5 &I
7. (P ∧ Q) → (P ∧ R) 2, 6 CP - 24P ⊢ Q → (P ʌ Q)1. P A
2. Q A
3. P ∧ Q 1,2 &I
4.Q→(P∧Q) 2,3CP - 25Give two examples of a binary predicate and for each, state whether it is reflexive, symmetric or transitiveP3
- 26Rxy x recognises y, Universe of discourse all the people in the room. Is it reflexive, symmetric or transitive?R is reflexive, not symmetric, not transitive.
- 27Everyone in the room recognises someone in the room∀x, ∃y st Rxy
- 28There is someone in the room whom everyone recognises∃x st ∀y, Ryx
- 29There is someone x who recognises everyone who recognises x∃xst∀y(Ryx→Rxy)
- 30For every number there is greater number∀x,∃y(y>x)
- 31Every number other than 0 is greater than some number∀x(¬(x = 0) → ∃y(x>y))
- 320 is the one and only number having the property that no number is less than it∀x(¬∃y(y
- 33X is equal to y (without using =)¬(xy)
- 34X is unequal to y(xy)
- 35Some girl won all the prizes∃x(girl(x) ∧ ∀y(prize(y) → won(x, y)))
- 36Each of the prizes was won by a girl∀x(prize(x) → (∃y(girl(y) ∧ won(y, x))))
- 37If any of the brakes hold, the train will halt∀x((brake(x) ∧ hold(x)) → train will halt)
- 38Brand x doesn't remove any kind of stain∀y(Stain(y) → ¬BrandXRemoves(y))
- 39Brand x doesn't remove all kinds of stain∃y s.t. (Stain(y) ∧ ¬BrandXRemoves(y)) or ¬∀y(Stain(y) → ¬BrandXRemoves(y))
- 40Different types of reasoning i)Induction, not valid
- 41Different types of reasoning ii)Deduction, valid
- 42Different types of reasoning iii)Abduction, not valid
- 43Different types of reasoning 1./
- 44Different types of reasoning 2./
- 45Different types of reasoning 3./
- 46Different types of reasoning 4./
- 47Different types of reasoning 5./
- 48Different types of reasoning 6./
- 49P → Q; P├ Q1. P → Q A
2. P A
3. Q 1,2 MPP - 50-Q → (-P → Q); -Q├ -P → Q1. -Q → (-P → Q) A
2. -Q A
3. -P → Q 1, 2 MPP - 51P → Q; Q → R; P ├ R1. P → Q A
2. Q → R A
3. P A
4. Q 1,3 MPP
5. R 2,4 MPP - 52P → Q; -Q├ -P1. P → Q A
2. -Q A
3. -P 1,2 MTT - 53P → (Q → R); P, -R├ -Q1. P → (Q → R) A
2. P A
3. -R A
4. Q → R 1,2 MPP
5. -Q 3,4 MTT - 54P → -Q; Q├ -P1. P → -Q A
2. Q A
3. - -Q 2 DN
4. -P 1,3 MTT - 55- P → Q; -Q├ P1. - P → Q A
2. - Q A
3. - - P 1,2 MTT
4. P 3 DN - 56P; Q├ P ∧ Q1. P A
2. Q A
3. P ∧ Q 1,2 &I - 57P ∧ Q├ P1. P ∧ Q A
2. P 1 &E - 58P → Q; P → -Q├ -P1. P → Q A
2. P → -Q A
3. P A
4. Q 1,3 MPP
5. -Q 2,3 MPP
6. Q ∧ -Q 4,5 &I
7. -P 3,6 RAA - 59Holmes can catch anyone who can catch Moriarty∀x (xCm → hCx)
- 60Holmes can catch anyone whom Moriarty can catch∀x (mCx → hCx)
- 61Holmes can catch anyone who can be caught by Moriarty∀x (mCx → hCx)
- 62If anyone can catch Moriarty, then Holmes can∃x (xCm) → hCm
- 63If everyone can catch Moriarty, then Holmes can∀x (xCm) → hCm
- 64Anyone who can catch Holmes can catch Moriarty∀x (xCh → xCm)
- 65Prove that: ∀x(Fx -> Gx), ∃x Fx├ ∃x Gx1. ∀x(Fx → Gx) (A)
2. ∃x Fx (A)
3. Fa (2, EE)
4. Fa → Ga (1, UE)
5. Ga (3,4, MPP)
6. ∃x Gx (5,EI) - 66∀x(Gx → Hx), ∃x (Fx ∧ Gx) ├ ∃x (Fx ∧ Hx)1.∀x(Gx → Hx) (A)
2. ∃x (Fx ∧ Gx) (A)
3. Fa ∧ Ga (2, EE)
4. Ga → Ha (1, UE)
5. Ga (3, ∧E)
6. Ha (4,5, MPP)
7. Fa (3, ∧E)
8. Fa ∧ Ha (6,7 ∧I)
9. ∃x (Fx ∧ Hx) (8, EI)
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- Argumentation and Computing (Logic) Flashcards on Logic Examples, created by Neja Cesnik on 30/04/2018.
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- Neja Cesnik
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