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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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