Examination Sheet № 18
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| Show that the set of reals is uncountable. Show that there is a bijection between the sets of all even natural numbers and the set of all integers.
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| Basic counting principles. The sum rule. The product rule. Principle of inclusion-exclusion. Number of all functions from a set A to a set B. The Pigeonhole principle. The Generalized Pigeonhole principle. Show that there are either three mutual friends or three mutual enemies in a group of six people, such that each pair of individual of the group consists of two friends or two enemies.
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| Construct the DNF, CNF and a polynomial for a proposition F (p, q, r) which is true iff (p, q, r) are from {(1, 1, 0), (1, 0, 0), (0, 0, 1), (0, 0, 0)}
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| How many ways to select 23 ordered elements from a set consisting of 54 elements are there, if repetition is not allowed?
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| Find a sequence { an: n = 0, 1, …} satisfying the recurrence relation xn + 6 = –6(xn –1 – 1) – 9 xn –2, with the initial conditions a 0 =1, a 1 = –9.
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Examination Sheet № 19
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| Set Operations. Venn Diagrams of all essential set operations. Set Identities. The cardinality of the union of two sets. Prove by Venn Diagram de Morgan laws.
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| Basic counting principles. The sum rule. The product rule. Principle of inclusion-exclusion. Number of all functions from a set A to a set B. The Pigeonhole principle. The Generalized Pigeonhole principle. Show that there are either three mutual friends or three mutual enemies in a group of six people, such that each pair of individual of the group consists of two friends or two enemies.
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| Construct the DNF, CNF and a polynomial for a proposition F (p, q, r) which is true iff (p, q, r) are from {(1, 1, 0), (1, 0, 0), (0, 0, 1), (0, 0, 0)}
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| How many ways to select 23 ordered elements from a set consisting of 54 elements are there, if repetition is not allowed?
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| Find a sequence { an: n = 0, 1, …} satisfying the recurrence relation xn + 6 = –6(xn –1 – 1) – 9 xn –2, with the initial conditions a 0 =1, a 1 = –9.
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2015-07-14
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