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Challenge Problems Question & Answer Key Resources SAT Questions Gaja Mathematics

SAT Questions Gaja Mathematics Challenge Problems

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B is a \(\textbf{subset} \) of a set A if every element of B is an element of A. For example, if \(A=\{a,b\}\), then all the subsets of A are \(\emptyset , \{a\}, \{b\}, \) and A (here\( \emptyset\) is the \(\textbf{emptyset},\) the unique set consisting of no elements). How many subsets does the set \(\{1,\ 2,\dots ,n\}\) have, where n is a positive integer?

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Question Type: Extended Constructed Response

Standard(s):HSN.RN.A.1

Standard Description: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3 = 5(1/3)3 to hold, so (51/3)3 must equal 5

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