#FocusOnExams : Philosophy GCE ‘A’Level – 23rd April 2020

Summary of the closest English Counterparts of truth-functional compound statement.

Negation: “It is not true that……..” or “it is false that…….”;  “it is not the case that…….”; “it is not……”;

Conjunction: and; but; however; while; although; yet; nevertheless; even though; though.

Disjunction: Either or; and/or; unless; neither…..nor….

Implication: If……..then; Given that..; assuming that…; provided that…; on the condition that …..; only        if…; is a sufficient condition for; is a necessary condition for.

Exercises on module 1

  1. which of the following symbolic statements have been poorly

punctuated? indicate the correct punctuations wherever necessary.

  1. (p>q>r) d)     ̴ ((p>q)>(r>s)
  2. (-p)>q)                                       e)   ̴  (    ̴pv    ̴q)
  3. (p>( ̰q>r)                                     f) (p.q). [(q.s). (r.p)]

 

  1. Put the following statements into symbols, by using the indicated letters.
  2. Vegetable is not good (G) if it is not fresh (F).
  3. The flowers will die off (F) unless it is watered (W).
  4. The students worked hard (S), yet they failed (F).
  5. John Bolt did not win(B) but Tayson Gay won(I).
  6. It is false that Gregory is old (G), but he is strong (S) and healthy (H)
  7. Either Chelsea was defeated (C) or Barca was defeated (B), but it is not true that both Chelsea and Barca were defeated.
  8. Using “A” as “Apartheid will be destroyed”, “M” as “Mandela fights for freedom” and “R” as “there will be respect of human Rights”, symbolize the following statements:
  9. If Mandela fights for freedom, then apartheid will be destroyed and there will be respect for human Rights.
  10. Either Mandela does not fight for freedom or apartheid is not destroyed.
  11. There will be respect for human rights if and only if Mandela fights for Freedom and apartheid be destroyed.
  12. If apartheid is not destroyed and Mandela does not fight for freedom, then there will be no respect for human rights.
  13. If either Mandela fights for freedom or Apartheid is destroyed, then there will be respect of human rights.
  14. Neither is Apartheid destroyed nor will there be respect of human Rights, if Mandela does not fight for freedom.
  15. By using the variables, p, q, r and s, express the following statements in symbolic forms.
  16. It is false that if exams are hard, then the students will fail.
  17. It is not the case both that man is good and wicked, unless he is determined and free.
  18. Discovery of the empty burse implied that the money had been collected.
  19. She is a Christian only if she has accepted Jesus Christ.
  20. Using the variables “T” as “trees are planted”, “I” as “increase in temperature”, “D” as “Depletion of the ozone layer” and “P” as “people will live longer”, express the following into ordinary language:
  21. ( ̴D)>P                               d) (T>  ̴I) . (D>  ̴P)
  22. TVI e) (P≡Tv   ̴D

̴T                                           f)   ̴(T>(DvP)

Therefore, T                                 ̴(D.P)

  1. ̴P≡D                                    therefore, T
  2. Given that A, B and C are true statements and X,Y and Z are false statements, which of the following are true?
  3.  ̴(BVX).   ̴(YVZ)                  d) [  ̴(  ̴CvY)v(  ̴YVC)]
  4.  ̴(CVB)V  ̴(  ̴Y)                e)    ̴[X.(  ̴AVZ)] v [(X.  ̴A)v(X.Z)]
  5.  ̴[(  ̴BVA) V (  ̴AVB)]       (f) {[(  ̴CVZ).(  ̴ZVC)].[(C.Z)V(  ̴C  ̴Z)]}
  6. Determine the truth-value of the following:
  7. [(p. q) v  ̴(pvq)]>q when both p and q are false
  8. ( ̴p .  ̴q)>q When p is and q is false
  9. Pv(p>q) when both p and q are false.
  10. [(p>(q>p)].  ̴p when p is true and q is false.

 

 

 

 

 

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