Math Help - Boolean Algebra Problems

1. Boolean Algebra Problems

Hi everyone! I almost find Boolean Algebra easy but I got confused with the laws. I need help again. It's my last week of Math 221.

Here are the laws:

I meant to follow them but there were variations in the problem questions, so I wasn't able to apply them.

2. Re: Boolean Algebra Problems

Hey jpab29.

For the ones you are having doubts/trouble with (like d) can you just show us the substitutions (using the values above) and the algebra for those?

3. Re: Boolean Algebra Problems

Thanks Chiro for replying! I'm still working on it, I'm applying the laws to the best of my understanding. I'll upload my work soon. This is question 1 of 12 questions of my homework.

4. Re: Boolean Algebra Problems

Here is what I did.
Can you please tell me which one I did correctly and which one I did wrong? Thanks. A correct answer for the wrong ones can be really helpful. Assignment due on Monday, so I still kind of have time to squeeze my brain out haha

Problem:

Solutions:

My copy of the laws:

5. Re: Boolean Algebra Problems

I have a feeling that I should not apply the laws on them, but I did it anyway... I also have a work without applying the laws, I just used the values and solved it as it is. What do you think? With laws or no laws?

6. Re: Boolean Algebra Problems

Is there a reason why you used distribution on b) instead of plugging in the values?

With regards to the laws, you usually use the laws when you don't have specific values for the binary variables. If you are given values, you just substitute these in and find the final answer.

If you have questions where you have to simplify the expression where you don't have actual values for the variables and are having problems completing these, then you should post these questions since these are the ones that are really testing your ability to know and apply the relevant boolean algebraic laws.

7. Re: Boolean Algebra Problems

Originally Posted by chiro
Is there a reason why you used distribution on b) instead of plugging in the values?

With regards to the laws, you usually use the laws when you don't have specific values for the binary variables. If you are given values, you just substitute these in and find the final answer.

If you have questions where you have to simplify the expression where you don't have actual values for the variables and are having problems completing these, then you should post these questions since these are the ones that are really testing your ability to know and apply the relevant boolean algebraic laws.
Thank you so much for clarifying that to me. My professor just also replied to just plug in the values (I persisted and persisted in asking him) but your answer is clearer than his. I have made another work, without applying the laws. If it's okay with you, or if you have time, please see if I did it correctly.

With my limited understanding of my textbook, and my reliance on YouTube, Ive become paranoid on the ways I should solve my assignment, so I tend to show 1 or 2 solutions.

8. Re: Boolean Algebra Problems

Hi again Chiro, I also have problem 2. It sounds kind of the same as problem one (highlighted text):

I don't have to apply the simplifying laws on it too? Just solve it like problem 1, but make a truth table and see which one comes out with a value of 1?

If I apply or don't apply the laws, will I still arrive at the same answer? because the laws simplifies the expression, therefore it should come up with the same answer right? As long as I did the simplifying correctly.

But if i don't need to do simplifying here, then I'll just redo my answers.

here's what I did, embarrassingly:

9. Re: Boolean Algebra Problems

Chiro, thank you so much for your help. My grades in math are actually dangerously failing, and week 5 (this last week) was my last chance. When I get the results back (hopefully I pass), I will post the answers I had here as help for future students who need.

Thanks again!