Hi, i've just started a degree in Computer Science and have a discrete math assignment to hand in tommorow. Could anyone please help?

(I'm not asking you to do it for me but explain how to do it or show me how to do 1 part in each question?)

These are the questions

1. Explain the difference between the following three offers, by analysing their logical form:

a) You can watch TV if you tidy your room

b) You can watch TV only if you tidy your room

c) You can watch TV if, and only if, you tidy your room

Which offer should a logical parent make to their children?

2. Construct the truth tables of the following compound formulas:

i) P => Q v R

ii) (P v Q) ^ (P => Q)

3. Use truth tables to show that the following formulas are always true:

i) P ^ Q <=> Q ^ P

ii) P ^ (Q v R) <=> (P ^ Q) v (P ^ R)

iii) ¬(P v Q) <=> ¬P ^ ¬Q

4. An enormous amount of loot has been stolen from a store. The criminal (or criminals) took the hesit away in the car. Three well known criminals A, B and C were brought to Scotland Yard for questioning. The following facts were ascertained:

a) No one other than A, B and C was involved in the robbery

b) C never pulls a job without using A (and possible others) as an accomplice

c) B does not know how to drive

Is A innocent or quilty?

[Hint: A way to answer this question is to rewrite the recorded facts using propositional logic, with basic statements of the form A is guilty, B is guilty, C is guilty, respectively. The next step wuld be to write down the truth tables for the formulas obtained. Keeping in mind that formulas representing facts are always true, you will then be able to deduce an answer tot he question.}