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Stevewh, Bachelor's Degree
Category: Calculus and Above
Satisfied Customers: 7386
Experience:  I teach Calculus and Probability in an University since 1994
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# Hi please I need an answer for the following questions: 1)

### Customer Question

1) Using the distributive laws, convert the formula (X_Y )^(W _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 :(X _ (Y ^ Z)) into disjunctive normal form.

3) (a) Show that the formula ((X ! Y ) ! X) ! 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?

Many thanks
Submitted: 1 month ago.
Category: Calculus and Above
Expert:  Stevewh replied 1 month ago.
Hi,

I do not understand some symbols

are you using a textbook ? which one ?

Thanks
Customer: replied 1 month ago.

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?

Expert:  Stevewh replied 1 month ago.
Yes, i understand them now

When do you need the answers ?

Thanks
Customer: replied 1 month ago.

By tomorrow?

Expert:  Stevewh replied 1 month ago.
Yes, sure

I will try to post the answers today, check this post later

Thanks
Customer: replied 1 month ago.

Great stuff! :-)

Expert:  Stevewh replied 1 month ago.
ok, check it tonight
Customer: replied 1 month ago.

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?

...and...

The regulations of the university state that: if a student achieves 40% in a course then the
student should pass that course. Mr Notquite achieved 39%. The board of examiners would like
to award him a pass anyway. Professor I. L. Logical, a member of sta who is not very good at
logic, thinks that the regulations prevent this.
Explain to Professor Logical why this argument is incorrect, by formulating both the regulation
and Professor Logical's belief as Boolean formulae and showing why they are not equivalent.

...thanks

Expert:  Stevewh replied 1 month ago.
Ok, i will look those too

Can you add a tip ?
Expert:  Stevewh replied 1 month ago.
Can you check 3) a)

I think is:

((X → Y ) → X) →X

Am i right ?
Customer: replied 1 month ago.

Hi Stevewh, yes that's right...

...cheers

Expert:  Stevewh replied 1 month ago.
Ok,

I finished the first 3 questions (1,2 and 3)

Now you added some questions to check ,can you add a tip of \$10 ?

Thanks
Customer: replied 1 month ago.

Yeah...

...let's get them done then!

Expert:  Stevewh replied 1 month ago.
Ok,

I will post the answers in less than 30 minutes

Thanks
Expert:  Stevewh replied 1 month ago.
Stevewh, Bachelor's Degree
Satisfied Customers: 7386
Experience: I teach Calculus and Probability in an University since 1994
Customer: replied 21 days ago.

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?

Expert:  Stevewh replied 21 days ago.
Yes, sure

Just open a new set writing "For Steve" and i will look them

Thanks

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