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Putnam
1972 Putnam
A2
A2
Part of
1972 Putnam
Problems
(1)
Putnam 1972 A2
Source: Putnam 1972
2/17/2022
Let
S
S
S
be a set with a binary operation
∗
\ast
∗
such that 1)
a
∗
(
a
∗
b
)
=
b
a \ast(a\ast b)=b
a
∗
(
a
∗
b
)
=
b
for all
a
,
b
∈
S
a,b\in S
a
,
b
∈
S
. 2)
(
a
∗
b
)
∗
b
=
a
(a\ast b)\ast b=a
(
a
∗
b
)
∗
b
=
a
for all
a
,
b
∈
S
a,b\in S
a
,
b
∈
S
. Show that
∗
\ast
∗
is commutative and give an example where
∗
\ast
∗
is not associative.
Putnam
Binary operation