Boolean algebra

Logic Level 1

Which of the following results true for x = y = 0 x=y=0 , a = b = 1 a=b=1 ?

( x b ) ( y b ) (x \wedge b)\vee (y\wedge b) ( x b ) ( a b ) (x \wedge b)\wedge (a\wedge b) ( x b ) ( a b ) (x \vee b)\vee (a\wedge b)

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1 solution

Eli Sutton
May 7, 2018

Using a substitution method, where x = y = 0 and a = b = 1, we get

a) (0 AND 1) OR (0 AND 1)

b) (0 AND 1) AND (1 AND 1)

c) (0 OR 1) OR (1 AND 1)

\hspace{10mm} simplifying (a) gives, 0 OR 0, which results in 0 = False

\hspace{10mm} simplifying (b) gives, 0 AND 1, which results in 0 = False

\hspace{10mm} simplifying (c) gives, 1 OR 1, which results in 1 = True

This is my first written solution. Apologies for the format/display. Share your solution, comments, and questions. Thank you kindly

Good explanation. Best I've seen.

Joseph Adkins - 2 years, 9 months ago

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