Matematika yasin

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Matematika yasin

  1. 1. QUESTIONS OF MATHEMATIC LOGIC
  2. 2. 1. If the statement is false and the statement p-value q true, then the following statement which is false is ... A. p ∨ q D. ~ P ∧ q B. p ⇒ q E. ~ P ∨ ~ q C ~ p ⇒ ~ q 2. Two statements p and q: P: is true Q: is false Compound statements below are true except: A. p ∨ q D. ~ P ∧ q B. p ∧ ~ q E. ~ (P ⇔ q) C ~ p ⇒ q
  3. 3. 4. Negation of the statement "All people eat rice "is: .. A. "Some people do not eat rice" B. "All people do not eat rice" C. "Not all people do not eat rice" D. "Not all people eat rice" E. "Some people eat rice“ 5. Negation of: "All the students did not make the task Mathematics "is ...... A. All students do not make the task matematics B. There are students who do not make the task matematics C. Some students make the task matematics D. Some students do not make the task matematics E. No student makes the task matematics
  4. 4. 5. The inverse of "if it rains then the road in front of the school muddy "is ... A. If the road in front of the rain did not tarnish the school down B. It did not rain and muddy road in front of the school C. If it did not rain the road in front of the school tarnish D. If it did not rain the road in front of the school does not tarnish E. It did not rain or road in front of the school is not tarnish 6.Statement equivalent to "If Amir diligent he's smart to learn it "is ... A. If Amir lazy to learn then he is stupid B. If Amir studious he is not smart C. If Amir does not study hard so he's smart D. If Amir was not good so he did not study hard E. If Amir was not good so he studied diligently.
  5. 5. 7. The convers of the phrase "If he was a Dutchman and he Europeans "are ..... A. If he is not European so he was not Netherlands B. If he is not then he is certainly the Netherlands Europe C. If it is not Dutch so he was not Europe D. If he is Dutch and he is not necessarily the Netherlands E. If he is a European so he is dutchman 8. Contraposition of (~ p ⇒ q) ⇒ (p ∨ ~ q) is .... A. (p ∧ q) ⇒ (p ⇒ ~ q) B. (p ⇒ ~ q) ⇒ (p ⇒ ~ q) C. (p ⇒ ~ q) ⇒ (p ⇒ q) D. (~ p ⇒ ~ q) ⇒ (p ∧ ~ q) E. (p ∧ ~ q) ⇒ (~ p ∧ ~ q)
  6. 6. 8. Contraposition of (~ p ⇒ q) ⇒ (p ∨ ~ q) is .... A. (p ∧ q) ⇒ (p ⇒ ~ q) B. (p ⇒ ~ q) ⇒ (p ⇒ ~ q) C. (p ⇒ ~ q) ⇒ (p ⇒ q) D. (~ p ⇒ ~ q) ⇒ (p ∧ ~ q) E. (p ∧ ~ q) ⇒ (~ p ∧ ~ q) 9. Conclusion of three premises: (1) p ⇒ q (2) q ⇒ r (3) ~ r A. p B. q C. r D. ~ p E. ~ r
  7. 7. 10. Inferences from the premises is….. A. p C. q E. ~ (p ∨ q) B. ~ p D. ~ q
  8. 8. 11. (~ pvq)^(pv ~ q) is equivalent to the statement .. a. p ⇒ q b. p ⇒ ~ q c. ~ p ⇒ q d. ~ p ⇒ ~ q e. p ⇔ q 12. q v ~ p statements are equivalent to the statement .. a. ~p ⇒~q b. q ∧ ~p c. ~q ⇒ ~p d. q ⇒ ~p e. ~q v ~p
  9. 9. 13. In the table below, the truth value for the column ~p ∧ ~ q from left to right are .. a. F T F F b. F F T T c. F F F T d. F T F T e. F T T T 14. The truth value of p ∧ ~ q are equivalent to the statement .. a. p ⇒ q b. ~ p ⇒ ~ q c. q ⇒ ~ p d. p ⇒ ~ q e. ~ ( p ⇒ q) p Q ~p ˄~ q T T T F F T F F
  10. 10. 15. The truth of (p ⇒ q) V ~q is equivalent with .. A. Tautology B. Contradiction C. ~p D. ~q E. (p V q)
  11. 11. THE ANSWERS ...
  12. 12. 1.To be able to answer the questions of logic, this table must understand (not memorize): Create a table for the above problem by basing the required table understood the above: which is false is ~ p ⇒ ~ q?  C
  13. 13. 2. Everything is true but there is a wrong one, we find that wrong. Create a table: Note: (P ⇔ q statement that is false is not answer as to facilitate the statement ~ (P ⇔ q) ) Seen from the table that is false is statement ~ P ∧ q?  D
  14. 14. 3.Remember! Quantifier sentence negation: ~ (all p) ⇒ no / some ~ p ~ (no / some p) ⇒ all ~ p - All negation is no / few - Eat rice ⇒ p = ~ p = not eat rice so its negation: no / some people do not eat rice. The answer is A
  15. 15. 4.- All existing negation / a - Do not make the task of curricular negation makes the task matematics So the negation of the sentence above: None / some students make the task cocuriculer The answer is C
  16. 16. 5. Theory: Konvers: p ⇒ q Inverse: ~ p ⇒ ~ q Contraposition: ~ p ~ q ⇒ Equivalence: p ⇒ q = ~ q ~ p ⇒ on the inverse problem means: p = if rain falls, ~ p = if it did not rain q = muddy road in front of the school, ~ q = road ahead school does not tarnish the answer is ~ p ⇒ ~ q: if it did not rain the road in front of the school is not tarnish The answer is D
  17. 17. 6.According to the theory Equivalence: p ⇒ q = ~ q ⇒ ~ p p = if Amir studious, ~ p = Amir did not study hard q = smart, ~ q = not smart the answer is: ~ q ⇒ ~ p if Amir doesn’t smart then Amir is not diligent the answer is D
  18. 18. 7.Convers: p ⇒ q p = the Netherlands, q = a European (Not required ingkaran sentence) then the answer is q ⇒ p : If he is a European Dutchman then he The answer is E
  19. 19. 8. Contraposition is ~ q ⇒ ~ p: Suppose p = (~ p ⇒ q) then ~ p = ~ (~ p ⇒ q) = ~ P ∧ ~ q This theory must be understood: negation: or: ~ (p ∨ q) = ~ p ∧ ~ q ..... (5) ~ (p ∧ q) = ~ p ∨ ~ q ..... (6) ~ (p ⇒ q) = p ∧ ~ q ..... (7) Suppose p = (~ p ⇒ q), ~ p = ~ (~ p ⇒ q) = ~ P ∧ ~ q (see .. (1) conditions remain p, q be the opposite) and turned into ∧ q = (~ p ∨ q), ~ q = ~ (~ p ∨ q) = P ∧ ~ q (see ... (5) p and q changes the sign of all, the operation turned into ∧ The answer is ~ p ~ q ⇒ namely: ⇒ p ∧ ~ q ~ p ∧ ~ q The answer is E.
  20. 20. 9. p ⇒ q q ⇒ r ~ r ∴? Step 1: p ⇒ q q ⇒ r ∴ p ⇒ r ? Sillogisme step 2: p ⇒ r ~ r ∴ ~ p? tollens the answer is D
  21. 21. 10. Equivalent: ~ p ∨ p ⇒ q ≡ q Then p ∨ q ≡ ~ p ⇒ q ≡ ~ q ⇒ p Statement negation p ∧ q ⇒ p ~ q ..... (1) q ⇒ p ∧ q ~ p .... (2) ~ p ⇒ ~ q ~ p ∧ ~ q ..... (3) ~ ~ p ~ q ⇒ p ∧ q ..... (4) becames: the answer is p (A)
  22. 22. 11. (~p v q) ^ (p v ~q) = T F F T E. p ⇔ q = T F F T The Answer Is E
  23. 23. 12. q v ~ p = F T T T Equivalent with d. q ⇒ ~p = F T T T
  24. 24. 13. So the answer is C P Q ~p ˄~ q T T F T F F F T F F F T
  25. 25. 14. p ∧ ~ q = F T F F EQUIVALENT WITH B. ~p ⇒~q = F T F F So the answer is B
  26. 26. 15. (p > q) v ~q T T T T F T F F T T F T T T F F T F T T THE ANSWER IS A (TAUTOLOGY)

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