Question

An ad for Herold's Gyro Shack claims that their gyros can be customized 1,024 different ways. An inspection of their menu reveals that they offer seven toppings for their gyros. Is their claim true or false? Provide an explanation using the language of set theory.

1) True
2) False

Answer 1

The claim that Herold's Gyro Shack can create 1,024 different customizations is false; there are only 128 possible combinations with seven toppings, considering the binary choice for each.

Step-by-step explanation:

The claim that Herold's Gyro Shack can customize their gyros in 1,024 different ways based on the seven toppings offered is false. To determine the total number of possible customizations using set theory, we can use the concept of combinations, where each topping can either be chosen or not, yielding two possibilities (2 choices) per topping. Since there are seven toppings, the total number of possible combinations is calculated as 2 to the power of 7, which is 27 or 128 different ways to customize a gyro. Therefore, the claim of 1,024 different customizations is not supported by the number of toppings provided.