logic和boolean algebra 的题目

oceanheng

1 Consider the following argument.
If Abu likes to drive to work or his father’s car is old, then he will buy a new car.
Abu does not buy a new car or he takes a train to work.
Abu did not take a train to work.
Therefore, Abu does not like to drive to work.
(a) Rewrite the argument using statement variables and connectives. [2 marks]
(b) Test the argument for validity. [5 marks]

2 Let set B with binary operations ∨ and ∧ be a Boolean algebra. Show that, for all x, y and z in B,
（X'∧Y'∧Z')∨(X'∧Y'∧Z)∨(X∧Y'∧Z)≡Y' [5 marks]

Allmaths

1 Consider the following argument.
If Abu likes to drive to work or his father’s car is old, then  ...
oceanheng 发表于 1-3-2012 11:05 PM

    (1)(a) p=Abu likes to drive to work

          q=Abu father’s car is old

           r=Abu will buy a new car

           s=Abu takes a train to work

          (p v q) → r

          ~r v s

          ~s

          ---------------

     ∴ ~p

     (b)用rule of inference, modus tollens, law of syllogism, simplification 就可以prove到了

(2)查一下题目有没有错误。

Allmaths

2 Let set B with binary operations ∨ and ∧ be a Boolean algebra. Show that, for all x, y and z in B,
（X'∧Y'∧Z')∨(X'∧Y'∧Z)∨(X∧Y'∧Z)≡Y' [5 marks]
oceanheng 发表于 1-3-2012 11:05 PM

    题目是不是少了这个？

（X'∧Y'∧Z')∨(X'∧Y'∧Z)∨(X∧Y'∧Z')∨(X∧Y'∧Z)≡Y'

oceanheng

回复 3# Allmaths
是是～copy error

Allmaths

回复  Allmaths
是是～copy error
oceanheng 发表于 2-3-2012 08:33 PM

    (X'∧Y'∧Z')∨(X'∧Y'∧Z)∨(X∧Y'∧Z') ∨(X∧Y'∧Z)
≡[(X'∧Y')∧(Z'∨Z)]∨(X∧Y'∧Z') ∨(X∧Y'∧Z)
≡[(X'∧Y')∧E]∨(X∧Y'∧Z') ∨(X∧Y'∧Z)
≡(X'∧Y')∨(X∧Y'∧Z') ∨(X∧Y'∧Z)
≡(X'∧Y')∨[(X∧Y')∧(Z'∨Z)]
≡(X'∧Y')∨[(X∧Y')∧E]
≡(X'∧Y')∨(X∧Y')
≡Y'∧(X∨X')
≡Y'∧E
≡Y'

oceanheng

回复 5# Allmaths


   proove 的是这样对吗？~r v s
~s
------------------
∴~r


(p v q) --> r
~ r
---------------------
∴~(p v q)


~p ^ ~q
∴~p