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)
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)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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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)
![0
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc2775e8c-94c2-43ee-8379-e9f8aff0b154%2F99851196-3991-48eb-8157-b4ea162b9475%2Fqdc724_processed.jpeg&w=3840&q=75)
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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
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