Let $C$ be the set of all ordered pairs $(x,y)$ satisfying $x^2 = 2^y$, where $x$ and $y$ are natural numbers. What is the cardinality of $C$?

✅ Correct Answer: 2

Explanation

Given $x^2 = 2^y$ Checking natural number solutions $(x,y) = (2,2)$ and $(4,4)$ satisfy the equation So the set has $2$ elements

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Let $C$ be the set of all ordered pairs $(x,y)$ satisfying $x^2 = 2^y$, where $x$ and $y$ are natural numbers. What is the cardinality of $C$? | ACME Academy