x y = 0 if and only if x = 0 or y = 0 • Assume that property 0 x = 0 is given Show that if x = 0 or y=0 then xy = 0 • Let p: x y = 0, q: x = 0 and r: y = 0, then the statement: If y=0 then x = 0 or y = 0 can be written as P⇒ (qVr) Argue that [p⇒ (qVr)] ⇒ [(p^~g) ⇒r] 1 . Based on the tautology above argue that it is sufficient to show that if x y = 0 and x #0 then y = 0. • Which basic property you are using to conclude that if x # 0, then there is a unique x¹ € F Start as follows y = 1.y = (x¹.x) y = x¹(x - y) = What do you need to use to conclude that y=0?
x y = 0 if and only if x = 0 or y = 0 • Assume that property 0 x = 0 is given Show that if x = 0 or y=0 then xy = 0 • Let p: x y = 0, q: x = 0 and r: y = 0, then the statement: If y=0 then x = 0 or y = 0 can be written as P⇒ (qVr) Argue that [p⇒ (qVr)] ⇒ [(p^~g) ⇒r] 1 . Based on the tautology above argue that it is sufficient to show that if x y = 0 and x #0 then y = 0. • Which basic property you are using to conclude that if x # 0, then there is a unique x¹ € F Start as follows y = 1.y = (x¹.x) y = x¹(x - y) = What do you need to use to conclude that y=0?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please answer both B and E
![b. x y = 0 if and only if x = 0 or y = 0
• Assume that property 0 x = 0 is given
Show that if x = 0 or y=0 then xy = 0
• Let p: x y = 0, q: x = 0 and r: y = 0, then the statement: If a y=0 then x = 0 or y = 0
can be written as
I⇒ (qVr)
Argue that [p⇒ (qVr)] → [(p^~g) ⇒T]
1
. Based on the tautology above argue that it is sufficient to show that if x y = 0 and x 0
then y = 0.
• Which basic property you are using to conclude that if x #0, then there is a unique ¹ F
. Start as follows
y = 1.y=(x-¹.x) y = x¹(x - y) =
What do you need to use to conclude that x y = 0?
. Finish your argument by showing that y = 0.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8d46346-fe9f-45aa-a3a0-df12b7cae379%2Fd1d30ede-baf7-4e69-bd11-2c020ea82363%2F8ilfspi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:b. x y = 0 if and only if x = 0 or y = 0
• Assume that property 0 x = 0 is given
Show that if x = 0 or y=0 then xy = 0
• Let p: x y = 0, q: x = 0 and r: y = 0, then the statement: If a y=0 then x = 0 or y = 0
can be written as
I⇒ (qVr)
Argue that [p⇒ (qVr)] → [(p^~g) ⇒T]
1
. Based on the tautology above argue that it is sufficient to show that if x y = 0 and x 0
then y = 0.
• Which basic property you are using to conclude that if x #0, then there is a unique ¹ F
. Start as follows
y = 1.y=(x-¹.x) y = x¹(x - y) =
What do you need to use to conclude that x y = 0?
. Finish your argument by showing that y = 0.
Transcribed Image Text:e. If 0<x<y then x² < y²
Show that x2 <ry - list the the basic property you are applying
Show that ry < y2 - list the the basic property you are applying
. Finish your argument by filling up all missing steps and putting the correct basic property
above each equality/inequality
V V
=
< so by
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