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Math Help - Boolean Algebra Truth Table for fundamental conjunction and dnf

  1. #1
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    Boolean Algebra Truth Table for fundamental conjunction and dnf

    Boolean Algebra Truth Table for fundamental conjunction and dnf-image.jpg

    Hello again! Can anyone help me understand how f, g and h got their column of answers from xyz columns? Is it thru multiplication or addition?

    Thanks.

    i would appreciate it if the explanation is in simple english, i am very poor with mathematical symbols. Need to
    understand this before i could move on with my assignment.

    I would understand the truth table if the examplr gave an expression like xy+z, then I'd solve for that because i'll know what to multiply and what to add. But the example above is just looking for fundamental conjunctions with a value of 1 and i don't know how f g h got their 1's and 0's.

    Thanks again!
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  2. #2
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    Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

    The functions f, g and h are just given. The fundamental idea of a function is that it is some way of converting an input into an output. Writing an expression with "and", "or" and "not" is just one way to define a Boolean function. We can use any means as long as it guarantees that every possible input is connected to a single output. In this case, f, g and h are given by explicitly listing their values for each input. The text says, "Let's consider these particular functions". Now, it turns out that every Boolean function can be specified by a Boolean expression, as in this example. This is not the case for functions on real numbers or even natural numbers. For example, the function that, given the coefficients a4, ..., a0 of a polynomial x5 + a4x4 + ... + a0 of degree 5 returns the smallest root of this polynomial cannot be expressed using the four arithmetical operations and roots.
    Thanks from jpab29
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  3. #3
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    Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

    So.... xyz was not calculated to get f and g all along? the textbook just put jumbled 0's and 1's on the f and g column with no calculation? and f(xyz)= ~x~yz =1 is also a given and I have to look into the table which is negatable in that way?

    hehe thanks
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  4. #4
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    Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

    I have to understand the example for me to be able to answer my assignment problems 4 and 5. Your explanation is waaaaay better than my instructor's:

    Indeed.

    Looking at one line... to explain....

    the second line has the values of x=0, y=0 and z=1

    in the explanation ... the function f is = x'y'z = x'*y'*z
    >> the terms are multiplied to gether

    the value of x' is 1
    the value of y' is 1
    the value of z is 1

    so the result of f = x'y'z = 1*1*1 = 1

    It would seem that you are not seeing how the functions f and g and h are described in the write up.

    Look clearly into the values of the functions...

    onward


    He didn't say that f values are given already. He just "rephrased" the example. Which I still don't get it, and yes he explains like that too, like a robot. It drives me crazy haha

    This is my assignment by the way:
    Boolean Algebra Truth Table for fundamental conjunction and dnf-exercise-15.1-problem-4-5.png

    This is what I did (don't mind the note I have on the bottom part, that's what I asked my professor again and again):

    Boolean Algebra Truth Table for fundamental conjunction and dnf-exercise-15.1-prob-4.jpg
    Last edited by jpab29; July 29th 2013 at 02:37 PM.
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  5. #5
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    Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

    So with my work uploaded, with w=x=0, y=z=1 given, I will automatically make put 1 on the f column where I see w=0, x=0, y=1, z=1, but then all zeros on other rows of f, right? Am i on the right track?
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  6. #6
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    Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

    When you said f is given, it gave me light!

    So what this guy is saying makes sense to me now:


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  7. #7
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    Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

    Quote Originally Posted by jpab29 View Post
    i have to understand the example for me to be able to answer my assignment problems 4 and 5. Your explanation is waaaaay better than my instructor's:

    indeed.

    Looking at one line... To explain....

    The second line has the values of x=0, y=0 and z=1

    in the explanation ... The function f is = x'y'z = x'*y'*z
    >> the terms are multiplied to gether

    the value of x' is 1
    the value of y' is 1
    the value of z is 1

    so the result of f = x'y'z = 1*1*1 = 1

    it would seem that you are not seeing how the functions f and g and h are described in the write up.

    Look clearly into the values of the functions...

    Onward


    he didn't say that f values are given already. He just "rephrased" the example. Which i still don't get it, and yes he explains like that too, like a robot. It drives me crazy haha

    this is my assignment by the way:
    Click image for larger version. 

Name:	exercise 15.1 problem 4 and 5.png 
Views:	5 
Size:	65.0 KB 
ID:	28927

    this is what i did (don't mind the note i have on the bottom part, that's what i asked my professor again and again):

    Click image for larger version. 

Name:	exercise 15.1 prob 4.jpg 
Views:	8 
Size:	622.5 KB 
ID:	28928

    wait!!! My truth table is wrong! Lol hahaha

    i'll redo it.

    w 1-8 should be 0 and 9-16 should be 1... And so the other columns i will redo. So sorry. Gosh i'm math drunk.
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  8. #8
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    Re: Boolean Algebra Truth Table for fundamental conjunction and dnf

    on second thought, I thought I got it wrong. hehehe It was my other assignment.

    emakarov, 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!
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