Simple Boolean Algebra / Propositional Logic Question

In summary: Being in the homework section does preclude just giving an answer. At least in my mind. But you did just fine on your own. Good work.
  • #1
sunmaz94
42
0

Homework Statement



Produce the given truth table (given below as well as in a neater version in the attached Excel document) using the Boolean operators AND, OR, and/or NOT:

A (Input 1) B (Input 2) O (Output)
1 1 0
1 0 0
0 1 1
0 0 0



Homework Equations



None; since AND, OR, and NOT are presumed knowledge.

The Attempt at a Solution



I tried taking the AND and OR of it and then taking the XOR (A AND (NOT B) OR ((NOT A) AND B)) of those results but that led me nowhere. I honestly have no idea how to proceed. Any help would be greatly appreciated. Feel free to express the solution (or parts thereof) in the conventional notation of logical conjunctions/disjunctions ([itex]\wedge[/itex] / [itex]\vee[/itex]) and negations ([itex]\neg[/itex]), if you prefer. Thanks!

P.S.

I am not using this for homework or coursework. It is actually for a circuit I'm building in the computer game Minecraft! So feel free to just give me a fully worked solution. :smile:
 

Attachments

  • Book1.xls
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  • #2
Probably best if you figure it out yourself, even if it's not a homework. This is after all the homework section. (A AND B) has one true outcome just like your example but it's in the wrong place. So that's a good place to start. Try putting a 'NOT' on the A or B.
 
  • #3
Dick said:
Probably best if you figure it out yourself, even if it's not a homework. This is after all the homework section. (A AND B) has one true outcome just like your example but it's in the wrong place. So that's a good place to start. Try putting a 'NOT' on the A or B.

I just figured it out. I was overcomplicated things unnecessarily. I see now that the answer is: [itex]\neg[/itex]A [itex]\wedge[/itex] B.

While I do thank you for your help, I would like to point out that the fact that: "This is after all the homework section", does not in any way preclude your ability to do it for me. That being said, I do agree with your general desire for the OP to figure things out themselves, with as minimal aid as possible.
 
  • #4
This thread is now solved. It can be locked. Thanks.
 
  • #5
sunmaz94 said:
I just figured it out. I was overcomplicated things unnecessarily. I see now that the answer is: [itex]\neg[/itex]A [itex]\wedge[/itex] B.

While I do thank you for your help, I would like to point out that the fact that: "This is after all the homework section", does not in any way preclude your ability to do it for me. That being said, I do agree with your general desire for the OP to figure things out themselves, with as minimal aid as possible.

Being in the homework section does preclude just giving an answer. At least in my mind. But you did just fine on your own. Good work.
 

1. What is Boolean Algebra?

Boolean Algebra is a branch of mathematics and logic that deals with binary variables and logical operations. It is used to analyze and simplify logical expressions or statements.

2. What are the basic operators in Boolean Algebra?

The basic operators in Boolean Algebra are AND, OR, and NOT. These operators are used to combine or manipulate binary variables in logical statements.

3. What is a truth table in Boolean Algebra?

A truth table is a table used to show the outputs of a logical statement for all possible combinations of input variables. It is used to determine the validity of a logical statement and can also aid in simplifying complex expressions.

4. How is Boolean Algebra used in computer science?

Boolean Algebra is an essential tool in computer science as it is the foundation of digital logic and circuit design. It is used to represent and manipulate binary data in computer systems and is also the basis for boolean search operations in databases.

5. What is the difference between Boolean Algebra and Propositional Logic?

Boolean Algebra and Propositional Logic are closely related, but there are some key differences. Boolean Algebra is a mathematical system used to manipulate and simplify logical expressions, while Propositional Logic is a formal system used to analyze the logical structure of statements. Additionally, Boolean Algebra deals with binary variables, while Propositional Logic can handle variables with multiple values.

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