Thank you, but I don't understand the "therefore" and which laws/identities were used. I've attached a chart of the Boolean laws/identities that are supposed to be used, step by step, to get from the starting expression to the finishing expression.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Chapter1: Introduction
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Thank you, but I don't understand the "therefore" and which laws/identities were used. I've attached a chart of the Boolean laws/identities that are supposed to be used, step by step, to get from the starting expression to the finishing expression.

TABLE 5 Boolean Identities.
Identity
=
X = X
x + x = x
X·X=X
x+0=x
x. 1 = x
x+1=1
x.0=0
x+y = y + x
xy = yx
x+y(y+z)=(x+y)+z
x(yz)=(xy)z
x+yz = (x+y)+(x+z)
x(y+z)=xy+xz
(xy) = x + y
(x+y)=xy
x + xy = x
x(x + y) = x
x+x=1
xx=0
Name
Law of the double complement
Idempotent laws
Identity laws
Domination laws
Commutative laws
Associative laws
Distributive laws
De Morgan's laws
Absorption laws
Unit property
Zero property
Transcribed Image Text:TABLE 5 Boolean Identities. Identity = X = X x + x = x X·X=X x+0=x x. 1 = x x+1=1 x.0=0 x+y = y + x xy = yx x+y(y+z)=(x+y)+z x(yz)=(xy)z x+yz = (x+y)+(x+z) x(y+z)=xy+xz (xy) = x + y (x+y)=xy x + xy = x x(x + y) = x x+x=1 xx=0 Name Law of the double complement Idempotent laws Identity laws Domination laws Commutative laws Associative laws Distributive laws De Morgan's laws Absorption laws Unit property Zero property
Expert Solution
Step 1
Starting with MX'Y+MXY'+M'XY+MXY, we can simplify the expression using Boolean laws/identities as follows:
  1. Distributive law: MXY' + M'XY + MXY = (MX + M' + M)XY' = MX'Y + M'XY'
  2. Commutative law: MX'Y + M'XY' = M'XY' + MX'Y
  3. Distributive law: M'XY' + MX'Y = (M' + M)X'Y = XY'
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Thank you, but I'm just not able to follow what is being done. It looks to me like the first minterm was left out of the initial step with no explanation as to why, and then it says MXY' + M'XY + MXY = (MX + M' + M)XY', but if I multiply out (MX + M' + M)XY', I get MXY'+M'XY'+MXY'. The M'XY' is not in the left side; so I don't see how this works. Then, later on, a complement law is mentioned, which does not exist in the chart, and there is no law/identity in the chart that matches going from XY' to X'+Y'. I apologize for being dumb here, but I'm just not following how you're getting from one expression to another. Could you please dumb it down even more for me. Thank you.

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