Consider the following statement: "We have a group of people consisting of 6 Ukrainians, 5 Poles, and 7 Slovaks. Some people in the group greet each other with a handshake (they shake hands only once). Prove that if 110 handshakes were exchanged in total, then two people of the same nationality shook hands". The proof below contains some missing phrases. From the lists below, choose correct phrases to form a complete and correct proof. Proof: We will estimate the maximum number of handshakes between people of different nationality. The number of handshakes between Ukrainians and Poles (Phrase 1). The number of handshakes between Ukrainians and Slovaks (Phrase 2). The number of handshakes between Poles and Slovaks (Phrase 3). Thus the total number of handshakes between people of different nationalities (Phrase 4). Since the total number of handshakes is 110, and (Phrase 4), two people of the same nationality must have shaken hands. QED Choose a correct Phrase 1: O is at most = 10 O is at least 5 O is at most 6² = 36 O equals 6 + 5 = 11 O is at most 6 · 5 = 30 Choose a correct Phrase 2: O equals 6 +7 = 13 O is at most 15 O is at least 7 O is at most 6 · 7 = 42 O is at least 6
Consider the following statement: "We have a group of people consisting of 6 Ukrainians, 5 Poles, and 7 Slovaks. Some people in the group greet each other with a handshake (they shake hands only once). Prove that if 110 handshakes were exchanged in total, then two people of the same nationality shook hands". The proof below contains some missing phrases. From the lists below, choose correct phrases to form a complete and correct proof. Proof: We will estimate the maximum number of handshakes between people of different nationality. The number of handshakes between Ukrainians and Poles (Phrase 1). The number of handshakes between Ukrainians and Slovaks (Phrase 2). The number of handshakes between Poles and Slovaks (Phrase 3). Thus the total number of handshakes between people of different nationalities (Phrase 4). Since the total number of handshakes is 110, and (Phrase 4), two people of the same nationality must have shaken hands. QED Choose a correct Phrase 1: O is at most = 10 O is at least 5 O is at most 6² = 36 O equals 6 + 5 = 11 O is at most 6 · 5 = 30 Choose a correct Phrase 2: O equals 6 +7 = 13 O is at most 15 O is at least 7 O is at most 6 · 7 = 42 O is at least 6
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:Consider the following statement: "We have a group of people consisting of 6 Ukrainians, 5
Poles, and 7 Slovaks. Some people in the group greet each other with a handshake (they
shake hands only once). Prove that if 110 handshakes were exchanged in total, then two
people of the same nationality shook hands".
The proof below contains some missing phrases. From the lists below, choose correct phrases
to form a complete and correct proof.
Proof: We will estimate the maximum number of handshakes between people of different
nationality. The number of handshakes between Ukrainians and Poles (Phrase 1). The number of
handshakes between Ukrainians and Slovaks (Phrase 2). The number of handshakes between
Poles and Slovaks (Phrase 3). Thus the total number of handshakes between people of different
nationalities (Phrase 4). Since the total number of handshakes is 110, and (Phrase 4), two
people of the same nationality must have shaken hands. QED
Choose a correct Phrase 1:
O is at most
= 10
O is at least 5
O is at most 6² = 36
O equals 6 + 5 = 11
O is at most 6 · 5 = 30
Choose a correct Phrase 2:
O equals 6 +7 = 13
O is at most
15
O is at least 7
O is at most 6 · 7 = 42
O is at least 6
Transcribed Image Text:Choose a correct Phrase 3:
O is at most 5 · 7 = 35
O is at most (6) = 21
O is at least 7
O is at least 6
equals 5 + 7 = 12
Choose a correct Phrase 4:
cannot exceed 30 + 42 + 35 = 107
is at most 6 · 5 . 7 = 210
O is at least 6 + 5 + 7 = 18
O equals 10 + 15 + 21 = 37
O is at most 11+13+12 = 36
Choose a correct Phrase 4:
O 110 < 210
O 107 < 110
O 110 > 37
O 37 > 36
O 210 > 107
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