Hello,  Could I please get help with this discrete maths question.  I'VE ATTACHED A PICTURE OF THE LOGIC SHEET BELOW: YOU CAN ONLY USE PROOFS 1-17!!!!!! Q1. Prove the following: [X v (Y ^ Z) ≡ (X v Y) ^ (X v Z)]  I've attempted the question myself and this is what I got, if someone could look through my question and see if it's correct, and if its incorrect could you please provide a walkthrough to how to do the problem in detail? that would be great. thank you.    My Attempt:  [X v (Y ^ Z) ≡ (X v Y) ^ (X v Z)]  Proof we observe for X,Y,Z LHS  X v (Y ^ Z)  X v (Y v Z) --- Golden Rule (11)  X v (Y v Z) --- V/V Rule (9)  (X v Y) v (X v Z) --- Golden Rule (11)  (X v Y) ^ (X v Z)

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Hello, 

Could I please get help with this discrete maths question.  I'VE ATTACHED A PICTURE OF THE LOGIC SHEET BELOW: YOU CAN ONLY USE PROOFS 1-17!!!!!!

Q1. Prove the following:

[X v (Y ^ Z) ≡ (X v Y) ^ (X v Z)] 

I've attempted the question myself and this is what I got, if someone could look through my question and see if it's correct, and if its incorrect could you please provide a walkthrough to how to do the problem in detail? that would be great. thank you. 

 

My Attempt: 

[X v (Y ^ Z) ≡ (X v Y) ^ (X v Z)] 

Proof we observe for X,Y,Z

LHS 

X v (Y ^ Z) 

X v (Y v Z) --- Golden Rule (11) 

X v (Y v Z) --- V/V Rule (9) 

(X v Y) v (X v Z) --- Golden Rule (11) 

(X v Y) ^ (X v Z) 

 

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= associative*
= symmetric*
= identity*
■ reflexive
true
v symmetric*
v associative*
v idempotent*
V/=*
V/EE
v/v
v zero
Golden Rule*
A symmetric
^ associative
A idempotent
A identity
absorption.0
absorption.1
V/A
A/V
A over=
A/==
strong MP
replacement
→ definition*
→ reflexive
→> true
➡V
A➡
shunting
⇒ to A=
⇒ over=
definition*
LAWS OF THE PREDICATE CALCULUS
false definition*
- over=*
- neg-identity
[(X=(Y=Z)) = ((X=Y)=Z)]
[X=Y=Y=X]
[X=true=X]
[X=X]
[true]
[Xv Y = YvX]
[Xv (YvZ) = (Xv Y) v Z]
[Xv X = X]
[Xv (Y=Z) = Xv Y = Xv Z]
[Xv (Y=Z=W) = Xv Y = Xv Z = Xv W]
[Xv (YvZ) = (XVY) v (Xv Z)]
[Xv true = true]
[X^ Y = X = Y = XvY]
[XAY = YAX]
[XA (YAZ) = (X^Y) ^ Z]
[X^X = X]
[X A true = X]
[X^ (XVY) = X]
[XV (X^Y) = X]
[XV (YAZ) = (XVY) ^ (X v Z)]
[XA (YV Z) = (X^ Y) V (X^Z)]
[XA (Y=Z) = X^ Y = X^Z = X]
[XA (Y=Z=W) = XAY = XAZ = XAW]
[X^ (X=Y) = X^Y]
[(X=Y) ^ (W=X) = (X=Y) ^ (W=Y)]
[X Y = Xv Y = Y]
[X→X]
[X→> true]
[X → XV Y]
[X^Y = X]
[XAY = Z = X…(Y=Z]
[X = Y = X^Y=X)
[X➡ (Y=Z) = XAY=X^Z]
[X+Y=X^Y = Y]
[X-Y = Y➡X]
[false=true]
[-(X=Y)=-X=Y]
[-X=X=false]
postulates are decorated with a
Transcribed Image Text:0 1 2 3 4 5 6 7 8 8a 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 = associative* = symmetric* = identity* ■ reflexive true v symmetric* v associative* v idempotent* V/=* V/EE v/v v zero Golden Rule* A symmetric ^ associative A idempotent A identity absorption.0 absorption.1 V/A A/V A over= A/== strong MP replacement → definition* → reflexive →> true ➡V A➡ shunting ⇒ to A= ⇒ over= definition* LAWS OF THE PREDICATE CALCULUS false definition* - over=* - neg-identity [(X=(Y=Z)) = ((X=Y)=Z)] [X=Y=Y=X] [X=true=X] [X=X] [true] [Xv Y = YvX] [Xv (YvZ) = (Xv Y) v Z] [Xv X = X] [Xv (Y=Z) = Xv Y = Xv Z] [Xv (Y=Z=W) = Xv Y = Xv Z = Xv W] [Xv (YvZ) = (XVY) v (Xv Z)] [Xv true = true] [X^ Y = X = Y = XvY] [XAY = YAX] [XA (YAZ) = (X^Y) ^ Z] [X^X = X] [X A true = X] [X^ (XVY) = X] [XV (X^Y) = X] [XV (YAZ) = (XVY) ^ (X v Z)] [XA (YV Z) = (X^ Y) V (X^Z)] [XA (Y=Z) = X^ Y = X^Z = X] [XA (Y=Z=W) = XAY = XAZ = XAW] [X^ (X=Y) = X^Y] [(X=Y) ^ (W=X) = (X=Y) ^ (W=Y)] [X Y = Xv Y = Y] [X→X] [X→> true] [X → XV Y] [X^Y = X] [XAY = Z = X…(Y=Z] [X = Y = X^Y=X) [X➡ (Y=Z) = XAY=X^Z] [X+Y=X^Y = Y] [X-Y = Y➡X] [false=true] [-(X=Y)=-X=Y] [-X=X=false] postulates are decorated with a
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