# Boolean algebra absorption law

## 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

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berkeman
Mentor

## 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...

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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?

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