Prove the boolean expression, Mathematics

Assignment Help:

Prove the subsequent Boolean expression:

(x∨y) ∧ (x∨~y) ∧ (~x∨z) = x∧z

Ans: In the following expression, LHS is equal to:  

(x∨y)∧(x∨ ~y)∧(~x ∨ z) = [x∧(x∨ ~y)] ∨ [y∧(x∨ ~y)] ∧(~x ∨ z)

= [x∧(x∨ ~y)] ∨ [y∧(x∨ ~y)] ∧(~x ∨ z)

= [(x∧x) ∨ (x∧~y)] ∨ [(y∧x)∨ (y∧~y)] ∧(~x ∨ z)

= [x ∨ (x∧~y)] ∨ [(y∧x)∨ 0] ∧(~x ∨ z)

= [x ∨ (y∧x)] ∧(~x ∨ z)  [x ∨ (x∧~y) =x]

= x ∧(~x ∨ z)   [x ∨ (x∧y) =x]

= [x ∧~x)] ∨ (x ∧ z)  [x ∨ (x∧~y) =x]

= 0 ∨ (x ∧ z) = (x ∧ z) = RHS


Related Discussions:- Prove the boolean expression

Jamal, jamal works every morning in his garden. yesterday he worked 3 AND 3...

jamal works every morning in his garden. yesterday he worked 3 AND 3-4HOURS. HE SPENT 1-3 OF THE TIME PULLING WEEDS. HOW MANY HOURS DID JAMAL SPEND PULLING WEEDS?

How many dollars did they raise the first two days, The freshman class is p...

The freshman class is participating in a fundraiser. Their target is to raise $5,000. After the first two days of the fundraiser, they have raised 32 percent of their goal. How man

Sums, what is 10 times 10 pls

what is 10 times 10 pls

representative value or an extreme value, A population forms a normal dist...

A population forms a normal distribution with a mean of μ=80 and a standard deviation of o=15. For every samples, compute the z-score for the sample mean and determine whether the

Addition involving negative numbers, Q. Addition Involving Negative Numbers...

Q. Addition Involving Negative Numbers? Ans. When you add together positive and negative numbers, there are essentially three possibilities that you can encounter. Let's e

Lesson 3.5 skills practice, Noah is renewing a magazine subscription. one p...

Noah is renewing a magazine subscription. one package offers to renew the magazine for 3 years for 26$. A second package offers to renew the magazine for 5 years for $38

What is 2^5, What is 2 5 ? 2 5 = 2 ×2 ×2 ×2 ×2 = 32

What is 2 5 ? 2 5 = 2 ×2 ×2 ×2 ×2 = 32

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd