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This problem trains for: SAT-I, AMC-8, GMAT, AMC-10.
If the operator ∇ is defined as:
which one(s) of the following choices is/are not equivalent to:
First of all, the expression is the product of two powers:
which eliminates choices II and IV. Choice IV is obviously incorrect since it assumes a ternary operator, whereas ∇ is a binary operator.
We must still verify the accuracy of both other expressions:
therefore, expression III is correct.
and expression I is also correct.