I'm reading through a logic + proof book and I thought I'd start a question thread for it as there's not many solutions to the exercises
----
http://en.wikipedia.org/wiki/List_of_logic_symbolsAnalyse the logical forms of the following:
1) We'll have either a reading assignment or homework problems, but we won't have both homework problems and a test. Let H be 'we'll have a homework assignment', R for the reading an T for the test.
My answer:
(R ⋀ T) ⋁ (R ⋀¬T) ⋁ H
Given answer:
(R ⋁ H) ⋀ ¬(H ⋀ T)
Obviously they're different but I wonder whether the way I wrote my answer is acceptable or not (or if I overlooked something and is just wrong).
Also, is this second part ¬(H ⋀ T) in this context interpreted as if there's homework, then there's no test? IS ¬(H ⋀ T) the same as ¬H ⋀ ¬T
----------------------
2) √(7) ≰ 2
My answer: ¬((√(7) < 2) ⋀ ( √(7) = 2))
The given answer used ⋁ rather than ⋀. I realise that that's because the symbol is 'not less than OR equal to' but since we already know that it's neither less than or equal to, couldn't we use and?
-------------
3) How would you analyze the logical form of '3 is a common divisor of 6, 9, and 15'? Would you just let a letter represent '3 is a common divisor of 6' and for the other two as well and write P ⋀ Q ⋀ R?
--------------
4) I'm stuck on these two:
Let S stand for the statement 'Steve is happy' and G for 'George is happy'. What English sentences are represented by the following:
a) [S ⋁ (G ⋀ ¬S)] ⋁ ¬G
b) S ⋁ [G ⋀ (¬S ⋁ ¬G)]
For a)
a) Either Steve is happy or George is happy and Steve is unhappy, or George is unhappy.
So if George is NOT unhappy, meaning he IS happy, then Steve is unhappy . If he is not unhappy, can Steve be happy? Does 'Steve is happy' alone imply that George is also happy? Or can we not say anything about that?
Thanks