1.2 Logical Operations - Simplifying Boolean Logic Part 1 Rules

Question 1

For this Segment there will be Constant and Alternating Values

Answer 1

Constant Values = 0, 1
Alternative Values = Letters(A, B, etc)

Question 2

What is Rule 1 - OR Identity Law?

Answer 2

OR operators with constant value of 0 such as A+0 will have the value of the Alternating value.
A+0=A

Question 3

What is Rule 2 - OR Annulment Law?

Answer 3

OR operators with a constant value of 1 such as A+1 will always have an end result of 1 no matter what.
A+1=1

Question 4

What is Rule 3 - OR Idempotent Law?

Answer 4

OR operators with both values being Alternating values will have the same value in both columns. If column A1 has 1 then Column A2 has 1. If column A1 has 0 then Column A2 has 0. That means the resulting value will be alternating
A+A=A

Question 5

What is Rule 4 - OR Inverse Law?

Answer 5

OR operators which have a positive and a negative version of a Alternating Value then the answer will always be 1 as whenever A1 is 1 A2 will be 0 and vise versa.
A+Ā=1

Question 6

What is Rule 5 - AND Annulment Law?

Answer 6

AND operators which have 0 as the constant value will always have a end result of 0 since both values can never be 1.
A.0=0

Question 7

What is Rule 6 - AND Identity Law?

Answer 7

AND operators which have 1 as the constant value can have a end result of 1 only is the alternating value is also 1. This makes it that the end result is dependant on A
A.1=A

Question 8

What is Rule 7 - AND Idempotent Law?

Answer 8

AND operators where both values are the same Alternating value will have an answer dependant on the Alternating Value. Either they are both 1 resulting in 1 or they are both 0 resulting in a 0.
A.A=A

Question 9

What is Rule 8 - AND Complement Law?

Answer 9

And Operators with a positive and negative alternating value can only have a end result of 0 as column A2 will always be opposite to column A1 so they will never be the same 1 value.
A.Ā=0

Question 10

What is Rule 9 - Double Complement Law?

Answer 10

Let’s say Ā = A’, Double Complement would be A’‘(A with 2 lines above it).
The end result is the opposite of an opposite so we opposite the opposite to get the original.
Opposite of A’ is A
A’’ = A

Question 11

What is Rule 10 - OR Absorptive Law?
E.g., A+(A.B)
You will Refer to this calculation throughout this answer.

Answer 11

E.g., A+(A.B)
If on both sides of an OR statement there is the same value and they have different operators (e.g. A+, A.) and there is a 2nd value(e.g. B) then it can be just simplified to the value on the left.
A+(A.B)=A
A+A.B=A
Since AND is more important than OR A+A.B is the same as A+(A.B)

Question 12

What is Rule 11 - AND Complement Law?
E.g., A.(A+B)
You will Refer to this calculation throughout this answer.

Answer 12

E.g., A.(A+B)
If there is the same value outside and inside the bracket(e.g. A outside the bracket and A inside the bracket.) and the operation inside and outside the bracket are different (e.g. . outside the bracket and + inside the bracket) then it simplifies to the value outside the bracket.
A.(A+B)=A
B.(B+A)=B
Since AND is more important than OR A.(A+B) is not the same as A.A+B