Mason98
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No Effort - Member warned that some effort must be shown
- Homework Statement
- Boolean algebra help
- Relevant Equations
- A.(a+b) = a
Proving a Logic Rule with Boolean Algebra: Step-by-Step Guide
- Context: Comp Sci
- Thread starter Mason98
- Start date
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- Tags
- Algebra Boolean algebra
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Gold Member
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What do you get when you use the distributive property here?
PS: Forum rules require you to show your attempt at a solution. We can only help by providing hints and pointing mistakes in your work.
PS: Forum rules require you to show your attempt at a solution. We can only help by providing hints and pointing mistakes in your work.
Mason98
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I thought it could possibly be A.B + A.C but I am not sure tbhcnh1995 said:
Gold Member
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Where is C in that expression?Mason98 said:
Mason98
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A.A + A.B i mean sorry, thanks for the help, i tried multiplying the brackets out
Gold Member
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Right.Mason98 said:
You need to use the laws of boolean algebra to simplify this expression. The distributive property was one of these laws. How will you reduce this further?
Can you find anything in your lecture notes?
Mason98
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Would i now use the Idempotent Law, which would change A.A to just A which would leave me with A +A.B and the A.B would change to B.A, so A + B.A ?cnh1995 said:
Gold Member
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Right.Mason98 said:
Then?
Gold Member
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No need to change A.B to B.A.Mason98 said:
Hint (if you haven't got the next step yet): A=A.1
Mason98
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Hmm thanks for the help by the way appreciate it :), I'm thinking it could be, A.1 + A.B?cnh1995 said:
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Now factor the expression, using the reverse of the distributive law. What do you get?Mason98 said:
Mason98
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A.(1+B)?Mark44 said:
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Right, and how can ##1 + B## be simplified? Remember that + is used for OR, so in terms of sets, this would be ##U \cup B##, where U is the universal set.Mason98 said:
Mason98
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1 + B is basically 1 or B? So, it can be simplified down to just 1? I'm so confused
Master1022
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Mason98 said:
Yes it can. If you think about the logic table for the expression [itex]1 + B[/itex], what is the outcome if [itex]B = 1[/itex]? What if [itex]B = 0[/itex]? Does it matter what [itex]B[/itex] is? That should help prove to you the identity [itex]X + 1 = 1[/itex] for a boolean variable [itex]X[/itex].
Another method when facing these problems is to use a Karnaugh map. These help when the logical expressions become more complex.
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Do you know how to make a logic table. If so, you should make one and if you have trouble, show your work.