Discrete Mathematics
Q211.
Let p, q, and r be propositions and the expression (p\rightarrowq)\rightarrowr be a contradiction. Then, the expression (r\rightarrowp)\rightarrowq isQ212.
Let a_{n} represent the number of bit strings of length n containing two consecutive 1s. What is the recurrence relation for a_{n}?Q214.
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 of the following is the negation of [\forall x, \alpha \rightarrow(\exists y, \beta \rightarrow(\forall u, \exists v, y))]Q218.
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 preciousQ219.
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?Q220.
Which of the following first order formulae is logically valid? Here \alpha(x) is a first order formula with x as a free variable, and \beta is a first order formula with no free variable.