Simple Boolean Algebra / Propositional Logic Question

[sunmaz94]

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 ($\wedge$ / $\vee$) and negations ($\neg$), 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.

 

[Dick]

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.

 

[sunmaz94]

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: $\neg$A $\wedge$ 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.

 

[sunmaz94]

This thread is now solved. It can be locked. Thanks.

 

[Dick]

I just figured it out. I was overcomplicated things unnecessarily. I see now that the answer is: $\neg$A $\wedge$ 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.