For each positive integer n , let P ( n ) be the sentence In any round-robin tournament involving n teams can be leaked T 1 , T 2 , T 3 , ... , T n , so that T i beats T i + 1 for every i = 1 , 2 , ... , n . a. Write P ( 2 ) . Is P ( 2 ) true? b. Write P ( k ) . c. Write P ( k + 1 ) . d. In a proof by mathematical induction that P ( n ) is true for each integer n ≥ 2 , what must be shown in the inductive step?
For each positive integer n , let P ( n ) be the sentence In any round-robin tournament involving n teams can be leaked T 1 , T 2 , T 3 , ... , T n , so that T i beats T i + 1 for every i = 1 , 2 , ... , n . a. Write P ( 2 ) . Is P ( 2 ) true? b. Write P ( k ) . c. Write P ( k + 1 ) . d. In a proof by mathematical induction that P ( n ) is true for each integer n ≥ 2 , what must be shown in the inductive step?
Solution Summary: The author explains that P (n) is the sentence in any round-robin tournament involving n teams.
For each positive integer n, let
P
(
n
)
be the sentence In any round-robin tournament involving n teams can be leaked
T
1
,
T
2
,
T
3
,
...
,
T
n
,
so that
T
i
beats
T
i
+
1
for every
i
=
1
,
2
,
...
,
n
.
a. Write
P
(
2
)
.
Is
P
(
2
)
true? b. Write
P
(
k
)
.
c. Write
P
(
k
+
1
)
.
d. In a proof by mathematical induction that
P
(
n
)
is true for each integer
n
≥
2
,
what must be shown in the inductive step?
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