Answer to Question #221675 in Discrete Mathematics for Sabelo Zwelakhe

Question

Use a Karnaugh map to simplify the following Boolean expression:

(x'$\land$ y'$\land$ z') v (x'$\land$ y'$\land$ z') v (x'$\land$ y'$\land$ z') v (x'$\land$ y'$\land$ z') v (x'$\land$ y'$\land$ z')

Answer 1

Let use a Karnaugh map to simplify the following Boolean expression:

$(x'\land y'\land z') \lor (x'\land y'\land z') \lor (x'\land y'\land z') \lor (x'\land y'\land z') \lor (x'\land y'\land z')$

A Karnaugh map is the following:

We conclude that this expression is equivalent to $x'\land y'\land z'.$ It follows also from the idempotent law: $p\lor p=p.$