PLEASE I NEED THE BEST OF THE BEST

I DONT WANT TO FAIL AGAIN PLS DO (answer it all complete solution) I NEED PEFECT SCORE PLS PLS

Complete the truth Table for the given statement by filling in the required columns 1. (P-Q)-(~PvQ) P Q P-Q ~P ~PVQ (P-Q)-(~PvQ) T T T F F T F F 2. (PV Q ) ~( ~PA~Q ) P Q PvQ P ~Q ~PA~Q (PV Q) (~PA~Q) T T T F F T F F 3. ( ~ PHQ ) - ( ~ P - - Q ) P ~P ~P- Q | ~ Q ~ P -- Q ( ~PHQ ) - ( ~ P -~ Q ) T T T F F T F FExample: (0 -+9) -1(9-0)~(0 -9)] enoifleoguig Isnobibnoold lov Construct the truth table for each of the following and show that the compound statement is tautology. a. (P-Q) + (~Q-*~P) D- KO - c. [PV(~P][Qv~Q] ansnod auboM .a b. ~(PAQ ) ( ~PV-Q) 4- -1(D-9) ~0-) enelloT auboM .a SOLUTION: a. 1(9 -0) +93 - 19- (09)] noitshogx3 .X 1. The dominant connective is >(0-9) noilisogetino9 to nollimogensit .8 2. Complete the columns P and Q 3. Combine columns 1 and 2 using connectivity -to get entries for P-Q noilibbA .8 4. Negate statement 3 to get entries in Column 4 5. Negate statement Q to get the entries in column 5 noitsoilifgmia .or 6. Combine columns 4 and 5 using the connective -to get entries for ~Q-~P. write the result in column 67. Finally combine column$ and 6 using the connective> to get the truth values for (P-Q)(-Q-P). write the result in column 73519 min P T Q ( P Q) PQtiv-Q- Pullsby (P= Q) +> ( ~Q -+~P) F T F F F T T Because (P-Q) (~Q-+~P) is all true, then the compound statement is tautology b. ~(PAQ ) +>( ~PV-Q) PDITAMIGHTAV UN373D 1. The dominant connective is ( 1/ 1/ AMV AG .214 :ondonot 159jdup. 2. Complete the columns P and Q 3. Combine columns 1 and 2 using the connectivex to get the entries for PAQ. . Negate column 3 to get the entries for ~(PAQ) 165 5. Negate statement P 6. Negate statement Q 7. Combine column 5 and 6 using the connectivev to get entries in"-PV-QW 8. Combine columns 4 and 7 using the connective> to get the truth values for ~(PAQ)(~PV-Q) isbasta insino P PAQ ~(PAQ) -P Q ~PV-Q -(PAQ)->(-PV-Q) 4:12. sonsmood 1 TI Bilnozell 120M T qmod grimsol T C. 1. the dominant connectivity is A ellid2 (ming.) "is complete the columns P and Q andmil lengo I 2sulsV 9107 negate statement P to get entries in column 3 SHAWN combine columns 1 and 3 using the connective v to get entries for column 4 negate statement Q to get entries in column S 6. Combines column 2 and 5 using the connectivev to get entries for column 6 7. Finally combine columns 4 and 6 using the connective , to get entries in column 7 P Q ~P Pv(~P) -Q I VEa F 1961 S VECI T I VECI ALTOT Since the entries under dominant connective are all true, then the statement Pv(~P][Qv~Q] is a tautology "List of Tautologles-+18 i Table 7 1. Associative: for (v) [(P v Q) v R] - [Pv (Q v R)] for ( ) (P A Q) ~ RJ - [PA (Q AR)] 2. Commutative: for (^) (PAQ) - (Q AP). for (v) (P VQ) - (Q v P) :noitiniloll : 3. Distributive: for () (PVQ)WRJ- (PAR)(QAR)G -YSCOURT for (v) . Law of blconditional propositions [(P - Q) ^ (Q-P)] - (P-Q) slamsx] Modus Ponens [PA (P Q)] - Q 1 - )+7 (0-9) .0 8. Modus Tollens [(-Q A (P- Q)] - -P 10- 7. Exportation (P Q) - R]-[P-(Q- R)] NOITU.102 8. Transposition or Contraposition "(P-Q)- Cal-pylounges mmmmob odT 9. Addition 1 915(qmo) 10. Simplification (P 1Q ) -P of rep on Jagad isle slugs al luzon ord show .4-4-(- 101 ashins ing of- svnownnoo 9di gaizu ? bos & anmulos saidmod11. Conjunction [(P) ~ (Q)]- (PAQ) O- q . 12. Double Negation VOITU 102 P- (-P) 21 Inomonte silodme onT s 13. Absorption (P- Q) - [P- (PAQ)] 14. Disjunctive Syllogism [(P v Q) A -P]- a [(P v Q) A -0]- P 15. Material Implication , on a Ingmus . ario. :(P- Q)- (-PM.Q).o mani writ meaning sd'T - fi noizulonos 16. Disjunctive Simplification " (PVP) - P 17. Resolution (Pv Q) A (-PVR) - (Q v R) momuzis to anmol babnate 18. Hypothetical Syllogism ((P -+ Q) (Q-R)] -(PR) ninoaseA too . 19. Constructive Dilemma [(P-Q)(R- S)in (PVR)- (QvS) 0+9 20. Destructive Dilemma ((P-Q) A (R-S)](-Qv-S)- (-Pv-R) earevni sill to voslist .s enGloT auboM 10 grunoessAl ovifieoqsuno) .S 0-9 0 - q Day 2. Valid Argument and Fallacy O- Argument q- : It is made up of two parts, the given statements called premises and a conclusion evilonizi(] .E It is valid if the conclusion is true whenever the premises are assumed to be true The argument that is not valid is said to be invalid argument or fallacy D v 9 D - Examples Premise 1: If one loves algebra, then he loves mathematics Premise 2: Mike love Algebra wait! . me pollya loiterlogyH 10 pnincassA eviliensiT .A Conclusion: Therefore, Mike love Mathematics 0 -9 Representing each simple statement with a letter P: One loves algebra A- 9-+9- Q: One loves mathematics Writing the premises and conclusion in symbolic form, we have: Premise 1: P-Q If one loves algebra, then he loves mathematics Premise 2: P Mike loves algebra Conclusion: - Q Therefore Mike loves mathematics To check whether the argument is valid or fallacy, we rewrite it as a conditional statement in the form [(P-Q)P]-Q and construct the truth table for the statement P Q P-+Q (P-QMP (P-Q)P]-Q T T F T F T Since the last column are all true, then the statement is tautology. Since the conclusion is true whenever the premises are true (first case), then the argument is valid. Note: If the conditional statement in the final column is false in the first case, then the argument is invalid or is a fallacy. And the statement is no longer tautology. Note that it is not a contradiction either. Use truth table to determine whether the symbolic form of argument is a tautology and whether it is valid or a fallacy a P-Q C. (PAQ)(QAP) : PVQb. ~P-+Q -Q nobonyjnoo .it . P (0 9) - 1(0) (9)1 SOLUTION: noijtpon s'duod .sr a The symbolic statement is [(P-Q)~p]--Q P Q P-+Q ~P (P-Q)A-P Q [(P-Q)-P]-Q T T F F F T F F F ICII F T s To T pollv svito F 210 .AT F F The entries in the last column are not all true, so the argument is not a tautology. And since the conclusion in row 3 is false while the premises are true, then the argument is a fallacy 9 - 19 v 9) noitsodilomid evilonjeid ar #b and c are left for students to do. Standard forms of arguments (8 . 0) - (8 . 9) ,10 9) Valid Argument 9) - [(8 -0), (0 - 9) Invalid Argument isoilgrtogyH 8t 1. Direct Reasoning or Modus Ponens 1. Fallacy of the Converse P- Q P - Q ammeld evilownlenoo or Q Q 8 3-1-2 -0-)112 - 2. Contrapositive Reasoning or Modus Tolens 2. Fallacy of the Inverse P- Q P- Q -Q -P zelle I bas inomugiA bileV .Sysd IngmugTA 3. Disjunctive Reasoning or Disjunctive Syllogism | 3. Misuse of Disjunctive Reasoning qu obst all 10 sili li bilBy 21 PvQ PvQ PvQ PvQ is insmugis bi laid insmugis andT -P -Q Q Q "dogls essol snoll I seimor 4. Transitive Reasoning or Hypothetical Syllogism | 4. Misuse of Transitive Reasoning P - Q P- Q Q- R Q- R P- R hrdsyls esvol and q -R - -P -P-~R