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

How many days are there in a year, There are m months in a year, w weeks wi...

There are m months in a year, w weeks within a month and d days in a week. How many days are there in a year? In this problem, multiply d and w to obtain the total days in one

Numercial analysis and computer techniques, write FORTRAN programme to gene...

write FORTRAN programme to generate prime numbers between 1 and 100

Method of disks or the method of rings, Method of disks or the method of ri...

Method of disks or the method of rings One of the simple methods for getting the cross-sectional area is to cut the object perpendicular to the axis of rotation.  Carrying out

Solve the fractional equation, Solve the fractional equation: Example...

Solve the fractional equation: Example: Solve the fractional equation 1/(x-2) +1/(x+3) =0 Solution: The LCD is (x - 2)(x + 3); therefore, multiply both sides of t

Defining real numbers, The numbers used to measure quantities such as lengt...

The numbers used to measure quantities such as length, area, volume, body temperature, GNP, growth rate etc. are called real numbers. Another definition of real numbers us

Pre Calc, Find reference angle alpha and thea element of [0 degrees, 1800 d...

Find reference angle alpha and thea element of [0 degrees, 1800 degrees]

Linear equation, The sum of the digit number is 7. If the digits are revers...

The sum of the digit number is 7. If the digits are reversed , the number formed is less than the original number. find the number

Angles, in the quadrilateral abcd,ab is 4.3,bd is 5.1,ad is 4.8.angle bdc i...

in the quadrilateral abcd,ab is 4.3,bd is 5.1,ad is 4.8.angle bdc is 20 degrees and angle c is 80 degrees.all dimentions in metres.calculate the unknown sides and angles of the plo

Find the middle term of the arithmetic progressions, Find the middle term o...

Find the middle term of the AP 1, 8, 15....505. A ns:    Middle terms a + (n-1)d = 505 a + (n-1)7 = 505 n - 1 = 504/7 n = 73 ∴ 37th term is middle term a 37

Comparing and scaling, a dairy mngr says it takes 70lbs of make 10 lbs of c...

a dairy mngr says it takes 70lbs of make 10 lbs of cottage cheese... How do I make a rate table and a make a graph showing the relationship between lbs of milk and lbs of cottage c

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