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Exercise 7-3: 3

Exercise 7-3: 3. Not all events have causes. It is not the case that for all x, if x is an event, then x has a cause. It is not the case that for all x, if Ex, then Cx ~(x)(Ex כ Cx). Exercise 7-3: 5. All natural events have causes.

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Exercise 7-3: 3

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  1. Exercise 7-3: 3 • Not all events have causes. • It is not the case that for all x, if x is an event, then x has a cause. • It is not the case that for all x, if Ex, then Cx • ~(x)(Ex כ Cx)

  2. Exercise 7-3: 5 • All natural events have causes. • For all x, if x is an event and x is natural, then x has a cause. • For all x, if Ex and Nx, then Cx • (x)[(Ex ∙ Nx) כ Cx]

  3. Exercise 7-3: 13 • There are no uncaused events, but there are events that are miracles. • For all x, if x is an event then it is not the case that x is uncaused, but for some x, x is an event and x is a miracle. • For all x, if Ex then it is not the case that not Cx, but for some x, Ex and Mx. • (x)(Ex כ ~~Cx) ∙ (x)(Ex ∙ Mx)

  4. Exercise 7-4: 11 • So if all logic students are logical, none of them is popular. • If for all x, if x is a logic student then x is logical, then for all, x if x is a logic student then it is not the case that x is popular. • If for all x, if Sx then Lx, then for all x, if Sx then not Px. • (x)(Sx כ Lx) כ (x)(Sx כ ~Px)

  5. Exercise 7-5: 3 • It's not true that there are overpaid athletes. • It is not the case that for some x, x is an athlete and x is overpaid. • It is not the case that for some x, Ax and Ox • ~(x)(Ax ∙ Ox)

  6. Exercise 7-6: 5 • Kangaroos and opossums are both marsupials. • For all x, if x is a kangaroo or x is a opossum, then x is a marsupial. • For all x, if Kx or Ox, then Mx • (x)[(Kx v Ox) כ Mx]

  7. Exercise 7-6: 11 • Female marsupials have pouches, but males don't. • For all x, if x is female and x is a marsupial then x has a pouch, but for all x, if x is male and x is a marsupial, then it is not the case that x has a pouch. • For all x, if Fx and Mx then Px, but for all x, if Lx and Mx, then it is not the case that Px • (x)[(Fx ∙ Mx) כ Px] ∙ (x)[(Lx ∙ Mx) כ ~Px]

  8. Exercise 7-9: 1 • Only those students who don't study regularly will flunk logic. • For all x, if x flunks logic, then x is a student and it is not the case that x studies regularly. • For all x, if Fx, then Sx and it is not the case that Rx • (x)[Fx כ (Sx ∙ ~ Rx)]

  9. Exercise 7-10: 9 • You have to be over 30 to enjoy Proust. • For all x, if x enjoys Proust, then x is over 30. • For all x, if Ex, then Ox • (x)(Ex כ Ox)

  10. Exercise 7-10: 15 • Scoundrels who aren't either brilliant or charismatic always are failures (don't succeed) in life. • For all x, if x is a scoundrel and it is not the case that x is brilliant or x is charismatic, then it is not the case that x succeeds in life. • For all x, if Sx and it is not the case that Bx or Cx, then it is not the case that Lx • (x){[Sx ∙ ~(Bx v Cx)] כ ~Lx}

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