liuxinyu95/unplugged

Chapter 1 - order of the exercises

liuxinyu95 opened this issue · 4 comments

liuxinyu95 commented

feedbacks:
“头几道习题的安排是不是再要考虑一下。我试下来乘法交换律和结合律的证明难度不比加法交换律低，而且证乘法结合律我用到了分配律。也就是——也许加法交换律应该放正文，并且习题2、3顺序应该反一下？”

liuxinyu95 commented

(1) first proof a.(b + c) = a.b + a.c

  • c = 0, a.(b+0) = a.b = a.b + a.0
  • suppose a.(b+c) = a.b + a.c holds, then
    a.(b+c')
    = a.(b+c)'
    = a.(b+c) + a
    = a.b + a.c + a
    = ab + a.c'
    QED

(2) proof (a.b).c = a.(b.c)

  • c = 0, (a.b).0 = 0 = a.0 = a.(b.0)
  • suppose (a.b).c = a.(b.c) holds, then
    (a.b).c'
    = (a.b).c + (a.b)
    = a.(b.c) + a.(b.1)
    = a.(b.c + b)
    = a.(b.c')
    QED
  • 👍1
liuxinyu95 commented

Will change the order of the exercise, and I am considering add an appendix of answers to some problems

  • 👍1