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Putnam
1971 Putnam
B1
B1
Part of
1971 Putnam
Problems
(1)
Putnam 1971 B1
Source:
4/6/2022
Let
S
S
S
be a set and let
∘
\circ
∘
be a binary operation on
S
S
S
satisfying two laws
x
∘
x
=
x
for all
x
in
S
,
and
x\circ x=x \text{ for all } x \text{ in } S, \text{ and}
x
∘
x
=
x
for all
x
in
S
,
and
(
x
∘
y
)
∘
z
=
(
y
∘
z
)
∘
x
for all
x
,
y
,
z
in
S
.
(x \circ y) \circ z= (y\circ z) \circ x \text{ for all } x,y,z \text{ in } S.
(
x
∘
y
)
∘
z
=
(
y
∘
z
)
∘
x
for all
x
,
y
,
z
in
S
.
Show that
∘
\circ
∘
is associative and commutative.
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