1. KL 2. (~N V~L) ^ (~M V ~O) 3. M⇒N 4. (ON)^(P⇒ L) (~M v ~K) ^ (~O V ~P)
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Please answe this problem, Inference rule. Show your solution. thank you
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- a. "p ^ q b. "p V q c. pV ^q d. pA~q e. p→ *q f. q→pGiven [ (p q) (q - r)]A (pA~r) 1. = [(-p v q)A(~qvr)]^(p^~r) 2. = [ ((-p v q) ^ ~q) v ((~p v q) An)JA(pA~r) 3. = [ ((-pA ~q) v (q A ~q)) v ((~p Ar)v (qAr) ]A(pA ~r) 4. = [ ((-p^ ~q) v F) v ((-p Ar) v (qan) ] ^ ( p^ ~r) 5. = [(-p^ ~q) v(~pAr) v (q A r)]A(p^~r) 6. = ((-p A ~q) A(p^~r)) v ((-p A r)^(p^~r)) v ((qan(r) 7. = (~p A ~q^ p^ ~r) v (~parap^ ~r) v (q Arap^~r) 8. = Fv Fv F 9. = F What is the process used to obtain line 4? (A) distributive law de Morgan's Law © identity law (D complement lawII. Let P= Mathematics is difficult. Q = PE is easy. B= Biology is interesting. Write each statement in words. 11. P^Q 16. -(P v Q) 12. Qv B 17.-(Q^ B) 13. -PA-B 18. P^(Qv B) 14. Q-B 15. B+-P 19. Pv (Q^ B) 20. Q^ (P→B)
- 2 1-z ze'dxdzdy o Jo Jo OA. e5 - 2 OB. Ов. Oc. e5 - 1 3 OD. e5 3Simplify (-nvq)-(n^q) to -n 1. Select a law from the right to apply (-nvq)^-(n^q) Distributive (a^b)v(a^c) (avb)^(avc) Commutative avb аль De Morgan's (аль) (avb) Conditional a→b a+b ||| ||| ||| ||| Laws a^(bvc) av(bлc) bva bдa -av-b -ал-Б avb =(a+b)^(b-a) Complement av ¬a = T алла Е F ¬T E -F ET Identity алт 3 а avF = a Double negation ла = aI. Determine whether the two given statements are equivalent. (YES or NO) 1. -P^-Q and~(P v Q) 2. P→Q and -P^Q 3. (P Q)^ (Q →P) and P+ Q Answer: Answer: Answer: 4. Pv (Q^ R) and (P v Q) ^ (P v R) Answer: 5. Pv (Q v R) and (P v Q) v R Answer: 6. P+ Q and P^ (P v Q) 7. -P v -Q and P^~Q 8. (P^Q) →R and (~P v-Q) v R Answer: Answer: Answer:
- 3. [pa(~q)]v[(~p)vq] In order to find the number of rows to create, use the formula 2", where n is the number of statements (letters). So, 22 = 4, so rows will be equal to 4. That is, %3D p^(~q) (~p)"q Tpa(~q)]| ~p V [(~p)vq] T T F F T F F The first two columns will be the standard truth value arrangements true to all statements that is equal to two.2. -P → (~Q ^P) P T F F F F