- #1
ZeroPivot
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Homework Statement
xy + compliment(xy) = 1
Homework Equations
The Attempt at a Solution
is it true? because x+compliment(x) = 1
maybe its not true...
Boolean Algebra Homework: Solving xy + compliment(xy) = 1
- Thread starter ZeroPivot
- Start date
In summary, The equation xy + compliment(xy) = 1 is true only if x and y are binary variables, and cannot be generalized to other values. The equation x+compliment(x) = 1 does not hold for all values of x. The equation xy + compliment(xy) = 1 and the equation x+compliment(x) = 1 are not equivalent and cannot be used interchangeably.
xy + compliment(xy) = 1
is it true? because x+compliment(x) = 1
maybe its not true...
- #2
CompuChip
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Yes. Take ##x + \overline{x} = 1## and rename x to a: ##a + \overline{a} = 1##.
Now set ##a = xy##.
Note, however, that ##\overline{xy} \neq \overline{x} \overline{y}##.
Now set ##a = xy##.
Note, however, that ##\overline{xy} \neq \overline{x} \overline{y}##.
- #3
ZeroPivot
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CompuChip said:
what if x=1 and y=0 the xy=0 and compliment(xy)=0 then 0+0 != 1
- #4
tiny-tim
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Hi ZeroPivot! 
(guys, thanks for the compliments, but it's complements!)
No, complement(xy) = 1
(guys, thanks for the compliments, but it's complements!
)ZeroPivot said:
No, complement(xy) = 1
- #5
ZeroPivot
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tiny-tim said:Hi ZeroPivot!
(guys, thanks for the compliments, but it's complements!
No, complement(xy) = 1
i meant compliment(x)compliment(y) = 0
but thanks.
- #6
tiny-tim
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Hi ZeroPivot!
So you meant, is ##xy + \bar{x}\bar{y} = 1## ?
No.
ZeroPivot said:
ZeroPivot said:
So you meant, is ##xy + \bar{x}\bar{y} = 1## ?
No.
- #7
CompuChip
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tiny-tim said:Hi ZeroPivot!
So you meant, is ##xy + \bar{x}\bar{y} = 1## ?
No.
Because if it were, ##\overline{xy}## would equal ##\bar x \bar y##. In fact it equals ##\bar x + \bar y##.
FAQ: Boolean Algebra Homework: Solving xy + compliment(xy) = 1
What is Boolean Algebra?
Boolean Algebra is a mathematical system used to analyze and manipulate logical expressions. It is based on the principles of Boolean logic, which deals with the truth values of statements and how they can be combined using logical operators.
What is the purpose of solving xy + compliment(xy) = 1 in Boolean Algebra?
The purpose of solving this equation is to determine the value of x and y that will make the statement true. This can be useful in simplifying logical expressions and solving problems in digital logic and computer science.
How do you solve xy + compliment(xy) = 1?
To solve this equation, you can use the laws and rules of Boolean Algebra, such as De Morgan's laws and the distributive property. First, you can rewrite the equation as xy + (x' + y') = 1. Then, you can use the distributive property to expand the expression and simplify it until you get a solution for x and y.
What are the possible values for x and y in Boolean Algebra?
The only possible values in Boolean Algebra are 0 and 1, which represent false and true, respectively. These values can be combined using logical operators to create complex expressions and statements.
Can Boolean Algebra be applied in real-world problems?
Yes, Boolean Algebra has many applications in computer science, digital electronics, and artificial intelligence. It is used to design and analyze digital circuits, create computer programs, and develop algorithms for decision-making systems.