Hi no sorry,
1) Using the distributive laws, convert the formula (X ORY ) AND (W OR Z) into disjunctive normal form.Check that your answer is equivalent to this formula by means of a truth table.2) Using the laws of logic, convert NOT (X OR (Y AND Z)) into disjunctive normal form.3) (a) Show that the formula ((X NOT Y ) NOT X) NOT X is a tautology.(b) Using the laws of logic we have studied, convert this formula into disjunctive normal form.Why does this help you to see why this formula is a tautology?
I have changed the symbols now, are they OK?
Great stuff! :-)
FOR Steve: could you also look at...
My answers so far in red…
Write a truth table for the Boolean formula (X → Y )AND NOT Y . Include the intermediate calculations
of (X →Y ) and NOT Y as in the incomplete example below:
X Y (X → Y ) NOT Y (X →Y ) ^ NOTY
t t T F F
t f F T F
f t T F T
f f T T T
Look at the lines of the truth table in which the outcome is true". What do you notice about
the values of X on those lines? Therefore not x – x is not true by contradiction
Now suppose I tell you that:
_ if it is raining when I get up in the morning, I pack my raincoat;
_ I did not pack my raincoat today.
What can you conclude about the weather when I got up today? It was not raining
…am I on the right track?
The regulations of the university state that: if a student achieves 40% in a course then thestudent should pass that course. Mr Notquite achieved 39%. The board of examiners would liketo award him a pass anyway. Professor I. L. Logical, a member of sta who is not very good atlogic, thinks that the regulations prevent this.Explain to Professor Logical why this argument is incorrect, by formulating both the regulationand Professor Logical's belief as Boolean formulae and showing why they are not equivalent.
Hi Stevewh, yes that's right...
...let's get them done then!
Hi Steve you answered some calculus questions for me a couple of weeks ago. I have a few more questions to ask around Sets! Let me know if you are able to answer them and I will forward them over to you?