1994 AHSME Problems/Problem 3
Problem
How many of the following are equal to for all
?
Solution
We look at each statement individually.
. We note that
. So statement
is true.
. We find a counter example which is
.
. So statement
is false.
. We see that this statement is equal to
.
is a counter example.
. So statement
is false.
. We see that
is again a counter example.
. So statement
is false.
Therefore, our answer is .
--Solution by TheMaskedMagician