Transcribe in digital format the following text NOW, (P₁-1) + (P₂-1) = P₁ + R₂-2 = P-2(P₁−1)²+(1₂-1)² + 2 (P-1) (P₂-1)= (P-2)² [Squaring bortsides]→ (P₁-1) ² + (₁₂-1) ² ≤ (P-2) ² [22 (1₁-1) (12-1) > 0]→ P₁² + P₂² - 2 (P₁+P₂) + 2 ≤ p²-4P+4== P₁² + P₂² ≤ p²-2p+2So, the maximus no.[²² P₁+₁₂=P]of edges in G= ²/²/2 [ P₁² + P₂²² -P] ≤But, given that,p²3p+222(P-1) (P-2)2G has more than (P-1) (P-2) edges.15ms,We get a contradiction.so, our assumption is wrong.Hence,G is connected (Prove) 9Given that, G is a graph of Orden p and his sizegreaten than (P-1)(P-1) (P-2)=22we have to show,ThenThe result is true orily whenG is Simple graphNow, Let us assume that G is not connected.G has at least two Connected Components.Say G₁ G₂9Suppose,then,P+P₂=Pas the graph is simple,andThe maximumThenG is connected.The Order of theРід P2graph G₁9 G₂ are P₁ 3 Pzrespectivelyso both G₁ 9. G₂ are Simple.of edges in Gi isPiCzPi (Pi-1)2+no of edges=so, the maximum sio. of edges in GP₁ (P₁-1)P2 (P₂-1).22; 1=1,2= = [₁²³+R² = (₁+B₂)] = { [9²6²³=P]-

Digital Format Now, P1 - 1 + P2 - 1 = P1 + P2 - 2 = P - 2⇒P1 - 12 + P2 - 12 + 2 * P1 - 1 * P2 - 1 =…

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Engineering

Computer Science

Transcribe in digital format the following text

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

Transcribe in digital format the following text

NOW, (P₁-1) + (P₂-1) = P₁ + R₂-2 = P-2
(P₁−1)²+(1₂-1)² + 2 (P-1) (P₂-1)
= (P-2)² [Squaring bort
sides]
→ (P₁-1) ² + (₁₂-1) ² ≤ (P-2) ² [22 (1₁-1) (12-1) > 0]
→ P₁² + P₂² - 2 (P₁+P₂) + 2 ≤ p²-4P+4
=
= P₁² + P₂² ≤ p²-2p+2
So, the maximus no.
[²² P₁+₁₂=P]
of edges in G
= ²/²/2 [ P₁² + P₂²² -P] ≤
But, given that,
p²3p+2
2
2
(P-1) (P-2)
2
G has more than (P-1) (P-2) edges.
15ms,
We get a contradiction.
so, our assumption is wrong.
Hence,
G is connected (Prove)

9
Given that, G is a graph of Orden p and his size
greaten than (P-1)
(P-1) (P-2)
=
2
2
we have to show,
Then
The result is true orily when
G is Simple graph
Now, Let us assume that G is not connected.
G has at least two Connected Components.
Say G₁ G₂
9
Suppose,
then,
P+P₂=P
as the graph is simple,
and
The maximum
Then
G is connected.
The Order of the
Рід P2
graph G₁9 G₂ are P₁ 3 Pz
respectively
so both G₁ 9. G₂ are Simple.
of edges in Gi is
PiCz
Pi (Pi-1)
2
+
no of edges
=
so, the maximum sio. of edges in G
P₁ (P₁-1)
P2 (P₂-1).
2
2
; 1=1,2
= = [₁²³+R² = (₁+B₂)] = { [9²6²³=P]
-

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