Home > College Algebra calculators > Boolean Algebra calculator

 Solve any problem (step by step solutions) Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
Problem: Is Boolean Algebra D10 [ Calculator, Method and examples ]

Solution:
Your problem -> Is Boolean Algebra D10

(1) Commutative laws
The following are the tables for +,* and '

 + 1 2 5 10 1 1 2 5 10 2 2 2 10 10 5 5 10 5 10 10 10 10 10 10
 * 1 2 5 10 1 1 1 1 1 2 1 2 1 2 5 1 1 5 5 10 1 2 5 10
 ' 1 2 5 10 10 5 2 1

From the tables it is clear that AA x, y in D_(10), x+yin D_(10) and x*yin D_(10)

:. + and * are binary operations.

The symmetry about the principal diagonal of first two tables indicates the commutative laws hold.

(2) Associative laws
We verify associative laws for 1,2 and 5
1+(2+5)=1+10=10

(1+2)+5=2+5=10

and
1*(2*5)=1*1=1

(1*2)*5=1*5=1

Similarly, it may be verified for other cases.

(3) Distributive laws
We verify distributive laws for 2,5 and 10
2+5*10=2+5=10

(2+5)*(2+10)=10*10=10

and
2*(5+10)=2*10=2

2*5+2*10=1+2=2

Similarly, it may be verified for other cases.

(4) Existence of identity elements
For the zero and unit elements, we check
1+1=1,1+2=2,1+5=5,1+10=10

10*1=1,10*2=2,10*5=5,10*10=10

:. 1 is the zero element and 10 is the unit element

(5) Existence of complement
1+1'=1+10=10 & 1*1'=1*10=1
2+2'=2+5=10 & 2*2'=2*5=1

1'=10,10'=1
2'=5,5'=2

:. (D_(10),+,*,',1,10) is a boolean algebra.

Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me