HW4-2.pdf - HWL‘ Jada” EW Lab 1 61/211!” ‘77(I(10...

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Unformatted text preview: HWL‘ Jada” EW Lab 1% 61/211!” ‘77 (I) (10 pts) Use natural deduction to prove the following argument: (aAb)/\c|-a/\C I (GAP—2.519 - 4 (mam rah?! % *aAAo qt -a - A ’52 E , l , /\ —- 5/ 3 M P a 2,5 (2) (10 pts) Use natural deduction to provegxe fo/\l}ow%g argumentA — I / l ’3 a,b,(a/\b)—)c|-c (4) (15 pts) Use natural deduction to prove the following argument: (fiaVb)—> -Id, a—H'. (z—ib, -nb l- -uch l (n. Ub)-r7cl 2 n-w 3 (-w-a’b .4 ., It is necessary to get at least a B in finite math to get accepted into Kelley. b -§ 0‘ You got less than a B in finite math. I Q l. You were not accepted into Kelley. "I b (a) (5 pts) Translate this argument into propositional logic. Carefully define the propositional variables you use. ‘ ~ _{ - ‘ l r r\ '7“ b: aCCGP—ltcl mic gem, ”hob (b) (10 pts) Prove that the argument is valid using natural deduction. b'fla/ "m l” 7b (6) Consider the following argument: IfI watch Superman, then I will eat popcornr’" b --> a I will eat popcorn if I was not on my phone .-\ I will not be on my phone if I watch Batman. 7( “a a b V d 1._ . ,, I will watch Batman or Superman, \ -——y '7 C I get popcorn 6/ d l) 9a (a) (5 pts) Translate this argument into propositional logic. Carefully define the 7 propositional variables you use. Cl'. '1' 1;.“ eari PIIPU’ln C I)“ ()1 PI gel b'. I back S'ufc‘n‘n ‘1 ""7 7" W66“ ,'. be 0 r“! WW6 cl f (l, b U A (b) (15 pts) Prove that the argument is valid using natural deduction. ‘l ‘ '7‘“ zw-rr'.,‘)Cr->a,cl ~57€ / boa l——'* 6 bair‘” o0 a l -b ”470‘ 1 ‘M —->/ a 3 a ,1, 7 c Ll __.....b Vii/“fl“ 5 12¢... - ‘ . . l7 b -->01. ' f C I ‘l l (7) Consuder the followmg argument: -7 ’1; ~90 ( e E i 2 g (i ”'9 «l L ( e314“; It’s too hot or it’s too cold! I). U l) r 6V : b ”>61“ If its too cold, 1’11 make a fire. q b V 3 E S S If I will feel like going outside and the pool' 18 open we’ll go SM Ae)~>f 4’ ’ I m not makin a fire. _/ g / We’re going swimming. {3' 7 [3 ——-—?(€ Nlfla) 5)pts )Translate this argument into propositional logic. Carefully define the propositional variables you use (7“ 14 5 490 Hal \l b l); 145 +00 co\d a 3131’“ K“ RC ‘- *“(t ‘lSLk Iv.“ ficei lté’ cm ou b”? C o it? o 9 j (lb) (15 pts) Prove that the argument is valid using eriaiural (iaeccluclionf 4‘: V6, 1 l (j 0 (JAG—ed 51 vi: 0M Hamlet/bet '16 7b ‘MCWl‘; gv'mn'wj "7C 2 (A nab—>15 7gng)5bac not .‘nc ...
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