Examination Sheet № 2

Examination Sheet № 1

Name:

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	Propositions. Logical Operations: negation, conjunction, disjunction, implication, exclusive or, biconditional. Truth Tables. Bitwise logical operations. Tautology and a contradiction. Prove that (p → (q → r)) → ((p → q) → (p → r)) is a tautology without using truth tables. Propositional Equivalences. Tables of Logical Equivalences.
	Recurrence relations. Solution of a recurrence relation. The tower of Hanoi. Codeword enumeration.
	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)}
	How many ways to select 23 ordered elements from a set consisting of 54 elements are there, if repetition is not allowed?
	Find a sequence {an : n = 0, 1, …} satisfying the recurrence relation xn + 6 = –6(xn–1 – 1) – 9xn–2, with the initial conditions a0 =1, a1 = –9.

 

 

Examination Sheet № 2

Name:

Surname:

Group:

 

	Truth Tables of basic logical operations. The number of all compound propositions consisting of n elementary compositions. Prove this by mathematical induction. Construct the truth table for the proposition .
	Generalized permutation and combinations. Permutations and combinations with repetition. Permutations of sets with indistinguishable objects, distributing objects into boxes.
	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)}
	How many ways to select 23 ordered elements from a set consisting of 54 elements are there, if repetition is not allowed?
	Find a sequence {an : n = 0, 1, …} satisfying the recurrence relation xn + 6 = –6(xn–1 – 1) – 9xn–2, with the initial conditions a0 =1, a1 = –9.