everything is in tabe just replace c list by their corresponding on page 503

\fDue by2359 hours on 20231114 Algorithm: (0) In the second row, fill in the I-values. (1) In the third row, use the entries in the Table in the above to replace each J-value by its corresponding connective, that is, C-value. (2) The last row is the list of connectives that you will use for this exam. J-nurnber nn--n--- C- values Connectivelist c: | c2 | c3 c4 c: (:6 c7 c3 \\ Egg mplg Algorithm: Finding the value of a formula using one's C-list. 0 To find the value of a formula written in terms of members of a C-list, replace each Cvalue by the corresponding connective as shown in this example using your own Clist. The formula in the below has been evaluated using the C-list in the example in the (P CEOI'D) Cs(('1p)55'?) (:9 ) (#1)) V((ap) v q) R All formulas on this test must be generated by this method. above: R Use the next algorithm to generate your Truth-Value Number 504 Due by2359 hours on 20231114 Truth-Value Number Your J-number Keep every 0 in your J-number and replace every non-zero number in your J-number by 1 to get Your (truth-value) T-number:= '8"1 9 YA auyall The := the kth entry in your truth-value J-number counting from the left. Therefore, T2 : T3 := TA # T5 := To : T7 : T8 := 505Due by2359 hours on 20231114 6 (1a) Find the truth-tables for after filling in the blanks appropriately: 2 (i) 01a(z)==('P 6km) C2 ((11064?) = (:9 HID) ((-49) q) (PCMJCsGCeT) (P Q) (9 7') 506 Due by2359 hours on 20231114 6 (1b) Find truth-tables for the following after filling in the blanks appropriately: 2(1) 15- ( 16 79 ) Car - ( " a ) " ) . 2 (ii) RS == pCar ) Cy ( acar - pr a r , and 2 (iii) decide, if LS :- (PC,q ) Car - PCar ) Cy (aCar -: R5 p q r pc7q (pc7q) Cor pCor qcor (pCor)C7(qCor) LS => RS p q r p q (p q) r pr q r (p r) (q r) LS = RS 0 0 0 0 0 1 0 1 0 0 1 1 10 0 1 1 1 1 1 - ( a ) . ( " ) ( 9 7 ) -ns Y N Pf W 507Due by2359 hours on 20231114 5 (1c) Decide, after filling in the blanks appropriately, if: PC 79 Cgr Vid Y N Pf W ( Dcar ) c. ( acar ) My problem: (1 9 ) Vid Y N Pf W (. " ) ( . . ) 509Due by2359 hours on 20231114 6 (2a) Find 4(p, q, r) in terms of p, q, r, and connectives, if o(p, q, r) is to have the following truth table: p r p ( p, q,r) 95 96 0 0 0 T1 = 0 1 T2 = 0 1 0 T3 = 1 1 TA = 1 0 0 T5 = 1 0 1 T6 = 1 1 0 T7 = 1 1 1 1 8 = 4 (p, q, r) S S 510Due by2359 hours on 20231114 6 (2b) Show work on pages that follow, properly numbered, to find, using the algebra of propositions, and the identities expressing p - q and p - q in terms of the connectives: -, V, and A to determine the equivalent expressions for y(p, q) as a disjunction of (conjunction of literals) (called DNF) and as a conjunction of (disjunction of literals) (called CNF). Cross out the disjuncts, respectively conjuncts, from the disjunctions and conjunctions provided in the lines marked DNF and CNF respectively so that equality holds. 4 (i) 4 (p, q) := -(P (79) ) (( IP) 9 ) ) = (PAq ) V DA ( 7 9 ) ) V ( IP ) NQ V ( TP ) A ( 79 ) ( DNF ) - (DV q ) A PV ( 79 ) ) 1 ( P ) Va A ( ( TP ) V ( -9 ) ( CNF ) 2 (ii) Fill in the column for y(p, q), using ONLY the columns of conjuncts (respectively disjuncts) as needed, on the basis of your answers to part (2b)(i). Fill in the last column from (la)(i). Wherever (p, q) has 0, 91a(1) should have 1 and vice versa. If this is not the case, something is wrong and 0 points will be awarded for both (la)(i) and (2b). p q -p 79 p A q p A (-q) ( -p ) A q pA ( -q) ( -p ) A ( -q ) y (p, q) Pia(i) 0 0 0 1 0 0 1 1 0 9 -p 79 p V q p V ( -q ) ( -p ) v q p v ( - q ) ( -p ) v ( -q ) 4 (p, q) Pia(ii) 0 0 1 1 0 1 1 10 1 0 0 1 1 1 10 511Due by2359 hours on 20231114 5 (2c) Show work on pages that follow, properly numbered, to decide, using the algebra of propositions, if the following inference is valid and circle the appropriate choice: PCsa - P PC39 - a Vid Y N Pf W ( DCza ) - (PCsa ) My problem: be (b a ) a r ba Vid Y N Pf W (0 9)- (1 9) 513Due by2359 hours on 20231114 6 (3a) Show work on pages that follow, properly numbered, to decide if the following proposition, denoted as indicated is a tautology, contradiction, or contingency, and circle an appropriate answer. 1 ( 1) a = (TC,P )C 3 1 ) = ( T P ) + ) Tig(a) Cdn(a) Cng(a) 1 ( 11) B = TC 2 ( PC 4 1 ) = T ( p 1 ) ) Tig (B) Can(B) Cng (B) 1 ( iii ) y = ( 1 Cap) CST = (1 p) T ) Tig(Y) Can(v) Cng (v) 1 (iv) 8= 1 CA ( PC 6 1 ) ) = 1 ( p n) ) Tig (8) Can(8) Cng (8) 1 ( V ) 3 TCs ( PC , 1 ) ) = T ( p 1 ) ) Tig(3) Cdn(3) Cng (5) 1 ( vi ) n = ( T Cop ) Ca + = ( T p ) + ) Tig(n) (u) up? Cng (n) 514Due by2359 hours on 20231114 6 (3b) Show work on pages that follow, properly numbered, to decide, using axioms and rules of inference, if the following inference is valid and circle the appropriate choice. If (2c) has been submitted, then the answer to (3b) must agree with the answer of (2c); otherwise, 0 points on both. (1'6"de (NH Vld Y N Pf w (pcgq)a(pc5q) My problem: Vld Y N 517 Due by2359 hours on 20231114 5 (3c) Fill in the gaps and decide if: p Cz q qcar rc6 s Vid Y N Pf W P C8 q My Problem: p q rr S Vid Y N Pf W 518