Sets, kinds of sets, algebra of sets, De-Morgan's laws; Cartesian product; relations, equivalence relations; functions, domain, codomain, range, invertible, even/odd, into/onto/one-to-one; special functions; sum, difference, product, composition.
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Q1 · Sets, Relations and Functions · MEDIUM
Let f: R → R be defined by f(x) = x³ + 2x² - 5x + 7. Let S = {x ∈ R : f(f(f(x))) = x}. Then which of the following is true?
Q2 · Sets, Relations and Functions · HARD
Let A and B be two finite sets with |A| = m and |B| = n. If the total number of subsets of A is 128 more than the total number of subsets of B, and the number of functions from A to B is 6561, then the value of m + n equals: