Which laws do I need to use to simplify

```
!X + (!Y + !Z)*(Y + Z)
```

to

```
!X + (Y*!Z) + (!Y*Z)
```

Answer:

You can first start by distributivity of multiplication over addition:

```
!X + (!Y + !Z)*(Y + Z) = !X + !Y*Y + !Z*Y + !Y*Z + !Z*Z
```

Then, we can use complementation to remove elements of the form `!p*p`

:

```
= !X + 0 + !Z*Y + !Y*Z + 0
```

And finally remove the `0`

as they are `+`

's neutral.

boolean-expression

I'm trying to do the Kmap for F(A,B,C,D)= A’B’C’D’+AC’D’+B’CD’+A’BCD+BC’D . I'm getting a little confused because not all the variable groupings have the same number of variables. some have 4 and some have 3. is this equivalent to F(A,B,C,D) = F(0,2,4,5,7) ? I don't know if you have to do...

compiler-construction,compiler-errors,boolean-expression

Hello I'm working on a domain specific language with my project group. We want to report to the language user if the predicate in for example if(predicate) or while(predicate) are always true or always false. The logic operators implemented on the language are AND, OR, NEGATION as well as the...

php,mongodb,aggregation,boolean-expression

My problem is that I need to express a condition in a Mongo Aggregation pipeline in the format ((A&B)||(C&D)) which when you write it out in the format that Mongo writes it's boolean expressions in yields {$or: {$and: {A, B}, $and: {C ,D}}. The problem with this is that you...

python,operators,boolean-expression

What's wrong with using not() in python?. I tried this In [1]: not(1) + 1 Out[1]: False And it worked fine. But after readjusting it, In [2]: 1 + not(1) Out[2]: SyntaxError: invalid syntax It gives an error. How does the order matters?...

ios,define,boolean-expression

I usually define my constants like so #define kIamAconstant and I have my api endpoint in a constant like this. Now my project requires me to have a toggle that switches this between two different end points for testing. I have a 10s of thousands of lines of code, and...

ruby-on-rails,ruby,boolean-expression

This might be a trivial point, but I don't understand it and it bothers me. Going through the Ruby on Rails Tutorial by Michael Hartl, there is this method definition : def create user = User.find_by(email: params[:session][:email].downcase) if user && user.authenticate(params[:session][:password]) log_in user redirect_to user else flash.now[:danger] = "Invalid email/password...

boolean-expression,simplification,boolean-algebra

Which laws do I need to use to simplify !X + (!Y + !Z)*(Y + Z) to !X + (Y*!Z) + (!Y*Z) ...

view,mariadb,simplification

I'm having a very weird problem with MariaDB 10, it simplify automaticaly some logical expression !! here's an example CREATE VIEW test AS SELECT 1 FROM test_table WHERE NOT (1 < 2 OR 3 > 4); SHOW CREATE VIEW test; CREATE ALGORITHM = UNDEFINED DEFINER =`root`@`localhost` SQL SECURITY DEFINER VIEW...

javascript,boolean,compare,boolean-expression

This question already has an answer here: chaining double equals == returns false 3 answers Let's var a = "first", b = "second", c = "first";. Expression a == c returns true, (of course!); a == c is true too. Then why does a == a == c return...

jquery,boolean-logic,boolean-expression

I have an object representing a player and let us say 2 players //create a player object function player(name,state,score) { this.name = name; this.state = state; this.score = score; } var players = [ new player('player1',true,0), new player('player2',false,0) ]; so I want the players to make a move one after...

java,string,validation,io,boolean-expression

I'm supposed to write a program that reads in a SSN as a string, including dashes, like DDD-DD-DDDD, where 'D' is a digit. If it's valid, it prints "valid ssn" and the opposite if it isn't valid. I'm supposed to have four methods: main, public static boolean validSSN(String s), public...

java,mouseevent,boolean-expression

I'm just starting to learn Java and I'm trying to correctly initialise 4 variables that come from a MouseEvent. I understand how to retrieve a click position, but I don't know how to create a boolean local variable, leftClicked, and initialize it to true if the left mouse button is...

vb.net,simplify,simplification

Consider I have some models as follow: black, green, blue, red. I have a function which receive an object and I would like to trycast the object to appropriate model. Now I have the code like this: Public Sub SetData(ByVal obj As Object) If TryCast(obj, black) IsNot Nothing Then Dim...

javascript,boolean-expression

I have to convert a number to comma format. E.g 12345 => 12,345. I have my solution : function convert(n) { n = n.toString(); var result = ''; var count = 0, var idx = n.length - 1; while (r = n[idx]) { count++; result = ((count % 3 ==...