1. Py --> [ (Qy ● Ry) v Sy ]
2. (Qy ● Ry) ---> ~ Py
3. Ty ---> ~ Sy
// (Py --> ~Ty)
Prove valid using the 18 rules of inference.
1. Py --> [ (Qy ● Ry) v Sy ] 2. (Qy ● Ry) ---> ~ Py 3. Ty ---> ~ Sy // (Py --> ~Ty) Prove valid using the 18 rules of inference.
Prove Valid: 1. (z)(Pz --> Qz) 2. (Ex) [(Oy • Py) --> (Qy • Ry)] 3. (x) (-Px v Ox) 4. (x) (Ox --> -Rx) ... :. (Ey) (-Py v -Oy) 1. (x) [(Fx v Hx) --> (Gx • Ax)] 2. -(x) (Ax • Gx) ..... :. (Ex) (-Hx v Ax) 1. (x) (Px --> [(Qx • Rx) v Sx)] 2. (y) [(Qy • Ry) --> - Py] 3. (x) (Tx --> -Sx) .... :. (y) (Py --> -Ty)
prove that the arguments are valid using rules of inference and laws of predicate logic, (state the laws/rules used) Væ(P(x) + (Q(x) ^ S(x))) 3x(P(x) R(x)) - - .. Ex(R(x) ^ S(x)) - - - (0)H-TE. - – – – – – (24-TE ((x)S_(w))XA ((x)S ^ ()04)XA (2) 1 (x)d)XA
The only 9 rules of inference allowed are: 1. Modus Ponens (MP) 2. Modus Tollens (MT) 3. Hypothetical Syllogism (HS) 4. Disjunctive Syllogism (DS) 5. Constructive Dilemma (CD) 6. Simplification (Simp) 7. Conjunction (Conj) 8. Addition (Add) 9 absorption SECTION ONE: Formal proofs of validity using natural deductions Prove the following argument valid using the nine rules of inference. Copy-and-paste key of symbols: • v - = i Argument Two (1) A5B (2) ( A B ) > C (3)...
need to solve using the 8 rules of inference 1.lv 2.-1 3. (-I v F) > () > M) 4.(MvH) > (S > 1) /S
[10 marks] Prove using the rules of inference that the premise Vx((W(x) v B(x)) A(W(x) B(x))) implies the conclusion Vx (-W(x)B(x))
Show that the following (formalized) arguments are valid by deriving conclusions from given premises by utilizing inference rules. the C 0 15 13] (51 [14] C AB 3: A V B Show that the following (formalized) arguments are valid by deriving conclusions from given premises by utilizing inference rules. the C 0 15 13] (51 [14] C AB 3: A V B
use 18 rules of inference to solve the following problem. Do not use conditional proof, indirect proof, or assumed premises.for each proof you must write the premises in that proof. 1. X v Y prove /S v Y 2. z 3.( x•z)---> s
3. Prove valid by a deductive proof: 1. S (TR) 2. R R 3. (V S)-(W T)/ .. V D~W 4. Prove valid by a deductive proof: 1. (B. L)VT 2. (BVC) (~LO M) 3.~M /.. T 5. Prove valid by a deductive proof: 1. E.(FVG) 2. (E.G)(HVI) 3. (~HV I)(E . F) /.. H= I
2. Starting from the four numbered premises below (which using only the rules of inference (including the instantiation and generalization rules) and the logical equivalences (as both were Make sure that you include both the rule and the line number(s) to which that rule is applied are assumed to be true) and presented in class), show that x E(x) (6 marks) 1) Vx A(x) AGB(x) 2) Эx С (x) — В (х) 3) Vx D(x) > с (х) 4) x...
DO NOT USE CP, IP, or AP in your proofs. I will not accept any proofs using CP, IP, or AP. Additionally, use only the 18 rules of inference found in the text and in the notes. If you use an inference rule such as Resolution or Contradiction, you will lose points. 2 (2) (f2p 02) (x) (Ox>-Rx) 2 (2) (f2p 02) (x) (Ox>-Rx)