Logical expressions?
Hello everyone, unfortunately I can't solve the problem. We're supposed to create a truth table from Boolean notation. Can anyone help me?
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Could someone please help me with the two tasks and the corresponding calculation and the result?
Good day Could someone please help me with the two tasks and the corresponding calculation and the result? Thanks so much !
It’s the stuff you’re looking at.
(/(A&B) & ((A&B)|C)) | ((A&B)|C) –> the first part is superfluous because X | (X & Y) = X. If (A&B)|C remains, D is always 1, if either A AND B or C 1 is.
The systematic approach has already been mentioned by the previous speakers. However, it can help to try to simplify the expression before the use of the variables.
First of all, you need to consider what all the possibilities for the truth values of A, B, C are you going through.
A can be true (w) or wrong (f)…
For each of the two cases (A true, A wrong) there are two cases in each case B (B true, B wrong…
There are two cases in each case: C (C true, C wrong…
Bzw, it’s more common to write this split up…
For each of the 16 cases one obtains a truth value D.
Now go through each of the lines and set the corresponding truth values for A, B, C in the given formula
and values the formula to the truth value for D to be obtained.
In the first case, for example (for A = w, B = w, C = w…
And so you go through each line, set the corresponding truth values for A, B, C a, calculate the truth value for D and put this truth into the table.
In the end, you should get the following table as a result…
===========
But… you can make life a little easier if you already know a few rules.
https://de.wikipedia.org/wiki/Boolesche_Algebra#Definition
In the concrete case, one could realize that one is an expulsion of form (a. 7.1 b)∨ b) have been present which are to be added with the aid of the absorption rule b) can simplify…
And with this simplified formula…
… it is then considerably less complicated to pass through all cases.
Possible values for a, b and c are 0 and 1.
etc. So a total of 8 lines in your table. Now you only have to determine the value of D for each line by calculating the individual values.