Validate the following arguments:
a. ( ~p ∧ ((q ∧ r) → s) ∧ (s → p) ∧ (~(q ∨ r) → t ) → t
b.( (p → r) ∧ q ∧ (q → ~r) ∧ r ) → ~p
1. Use the DPP to decide whether the following sets of clauses are satisfiable. (a) {{¬Q,T},{P,¬Q},{¬Q,¬S},{¬P,¬R},{P,¬R,S},{Q,S,¬T},{¬P,S,¬T},{Q,¬S},{Q,R,T}} (b) {{¬Q,R,T},{¬P,¬R},{¬P,S,¬T},{P,¬Q},{P,¬R,S},{Q,S,¬T},{¬Q,¬S},{¬Q,T}} 2. Decide whether each of the following arguments are valid by first converting to a question of satisfiability of clauses (see the Proposition), and then using the DPP. (Note that using DPP is not the easiest way to decide validity for these arguments, so you may want to use other methods to check your answers) (a) (P → Q), (Q → R),...
5. Let P, Q, and R denote distinct propositional variables. Which of the following arguments are valid? Justify your answer. (a) (P+Q), Q+ R), therefore (-PVR). (b) ((PAQ) + R), P, R, therefore Q.
Use propositional logic to prove the validity of the following arguments: a) (P -> Q) -> (Q' -> P') b) [(P∧Q) -> R] -> [P -> (Q -> R)]
Please give proof direct or indirect with numbered justification/law. (a) t→r, ¬(r∨¬q), ¬t→p, p→(s∨¬q) ⇒ s (b) (s→q)∧(p→t) ⇒ (s∨p)→(q∨t)
Example 1. RP 2. Q R 1:: Q = P. Answer 11. RP 2. Q R 3. Q->P (Premise) (Premise) /.. Q->P [1, 2, CA Construct deductions for each of the following arguments using Group I rules. (4) es 1. P 2. (R & S) v Q 3. NP "QI.. "(R & S) 1. P 2. "(R & S) VQ 3.`p NQ 4 5. (Premise) (Premise) (Premise)/A MR & S) If
A normal chromosome has the following sequence: L M N O o P Q R S T (o = centromere). Name the type of chromosomal aberration present in each of the following chromosomes which arose from the original sequence shown above, being as specific as possible. Then draw how the chromosomes line up during meiosis L O o P Q R S T: L M N O o P Q R S T: L M N Q P o O...
[~[p n ~q] n [~r U s]] > [[[s>q] n ~p] > ~r]
Answer 1. RP 2. Q R 3. Q->P (Premise) (Premise) /..Q->P 1, 2, CA Construct deductions for each of the following arguments using Group I rules. (1) nces 1. PS 2. PvQ 3. QR/..SvR 1. PS 2. PvQ 3. Q R 4. (Premise) KPremise) (Premise) //. SVR
3. (Logic) Answer the following questions: Construct the truth table for (p rightarrow r) (q rightarrow r) doubleheadarrow (p q) rightarrow r Is the following argument valid? (r s) (q s) s rightarrow (p r) rightarrow t) t rightarrow (s r) p rightarrow r
N 3. Q+ "S 4.PNS 5. NS "R 6. PMR KPremise)/:P "R 1, 3, CA 2, CONTR 4, 5, CA mts Identify which Group I or Group II Rule was used in Deductions. (2) Ask Print 1. P - Q (Premise) 2. R - ("S v T) (Premise) 3. p R (Premise)/: ("Q & S) T 4.NQ NP 5. "Q R 6. "Q ("S v T) 7. "Q ( ST) 8. ("Q & S) T References (Premise) |(Premise) (Premise)/: ("Q...