Discrete Mathematics
Q211.
Let a_{n} represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for a_{n}?Q212.
Let p, q, and r be propositions and the expression (p\rightarrowq)\rightarrowr be a contradiction. Then, the expression (r\rightarrowp)\rightarrowq isQ214.
Which one of the following options is CORRECT given three positive integers x, y and z, and a predicate P(x)=\neg (x=1)\wedge \forall y(\exists z(x=y*z))\Rightarrow (y=x)\vee (y=1)Q215.
Consider the following logical inferences. I1: If it rains then the cricket match will not be played. The cricket match was played. Inference: There was no rain. I2: If it rains then the cricket match will not be played. It did not rain. Inference: The cricket match was played. Which of the following is TRUE?Q216.
Suppose the predicate F(x,y,t) is used to represent the statement that person x can fool person y at time t. which one of the statements below expresses best the meaning of the formula \forall x \exists y \exists t(\neg F (x, y, t))?Q217.
Which one of the following is the most appropriate logical formula to represent the statement? "Gold and silver ornaments are precious". The following notations are used: G(x): x is a gold ornament S(x): x is a silver ornament P(x): x is preciousQ218.
Which of the following is the negation of [\forall x, \alpha \rightarrow(\exists y, \beta \rightarrow(\forall u, \exists v, y))]Q219.
Let fsa and pda be two predicates such that fsa(x) means x is a finite state automaton, and pda(y) means that y is a pushdown automaton. Let equivalent be another predicate such that equivalent (a, b) means a and b are equivalent. Which of the following first order logic statements represents the following: Each finite state automaton has an equivalent pushdown automatonQ220.
Consider the following well-formed formulae: I. \neg \forall x(P(x)) II. \neg \exists x(P(x)) III. \neg \exists x(\neg P(x)) IV. \exists x(\neg P(x)) Which of the above are equivalent?