How Does the Absorption Law Simplify This Boolean Function?

[Lilia]

Homework Statement

i'm viewing an example written in class. it looks like this:

f(x₁, x₂, x₃, x₄) = [(not x₁) * x₂ * x₄] ∨ [x₂ * x₃ * x₄]

what should be function after applying absorption law?

Homework Equations

i know how another option called "gluing" works:

[x₁ * x₂ * x₃] ∨ [(not x₁) * x₂ * x₃] = x₂ * x₃

The Attempt at a Solution

our teacher wrote f(x₁, x₂, x₃, x₄) = x₂ * x₃ * x₄ but I'm having a hard time to understand why

 

[berkeman]

Homework Statement

i'm viewing an example written in class. it looks like this:

f(x₁, x₂, x₃, x₄) = [(not x₁) * x₂ * x₄] ∨ [x₂ * x₃ * x₄]

what should be function after applying absorption law?

Homework Equations

i know how another option called "gluing" works:

[x₁ * x₂ * x₃] ∨ [(not x₁) * x₂ * x₃] = x₂ * x₃

The Attempt at a Solution

our teacher wrote f(x₁, x₂, x₃, x₄) = x₂ * x₃ * x₄ but I'm having a hard time to understand why

From: https://www.electronics-tutorials.ws/boolean/bool_6.html

• Absorptive Law – This law enables a reduction in a complicated expression to a simpler one by absorbing like terms.
• • A + (A.B) = A (OR Absorption Law)
  • A(A + B) = A (AND Absorption Law)

Are you sure you typed the question right? The form of your equation doesn't seem to match the OR form of the Absorptive Law...

 

[Lilia]

now i see.

we were writing quine-maccluskey algorithm example, and we applied this law because in coverage matrix (quine matrix) there was no column with single 1.

this is the matrix:
-------------------------------------------------
implicant | 0111 | 1100 | 1110 | 1111 |
-------------------------------------------------
01-1 ...|...1...|...|...|...|
-------------------------------------------------
-111 ...|...1...|...|...|...1...|
-------------------------------------------------
111- ...|...|...|...1...|...1...|
-------------------------------------------------
--00 ...|...|...1...|...|...|
-------------------------------------------------
1--0 ...|...|...1...|...1...|...|
-------------------------------------------------
first and second row is my question. but now i think i get it.

since second row covers two 1s, and the first row - one 1, that's why it's called absorption
in the same manner 5th absorbs the 4th one, and the result is [x₁ * (not x₄)] (as our teacher wrote)

am i right?