Discrete Mathematics
Q191.
The statement (\neg p)\Rightarrow (\neg q) is logically equivalent to which of the statements below? I. p\Rightarrow q II. q \Rightarrow p III. (\neg q)\vee p IV. (\neg p)\vee qQ192.
Let a_{n} be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of the following is the recurrence relation for a_{n}?Q193.
Consider the statement "Not all that glitters is gold" Predicate glitters(x) is true if x glitters and predicate gold(x) is true if x is gold. Which one of the following logical formulae represents the above statement?Q194.
What is the correct translation of the following statement into mathematical logic? "Some real numbers are rational"Q195.
Geetha has a conjecture about integers, which is of the form\forall x\left [P(x)\Rightarrow \exists yQ(x,y) \right ] where P is a statement about integers, and Q is a statement about pairs of integers. Which of the following (one or more) option(s) would imply Geetha's conjecture?Q197.
Consider the first-order logic sentence \varphi \equiv \exists s\exists t\exists u\forall v\forall w\forall x\forall y\varphi (s,t,u,v,w,x,y) where \varphi (s,t,u,v,w,x,y) is a quantifier-free first-order logic formula using only predicate symbols, and possibly equality, but no function symbols. Suppose \varphi has a model with a universe containing 7 elements. Which one of the following statements is necessarily true?Q198.
Consider the following two statements. S1: If a candidate is known to be corrupt, then he will not be elected S2: If a candidate is kind, he will be elected Which one of the following statements follows from S1 and S2 as per sound inference rules of logic?Q199.
Let p, q, r denote the statements "It is raining ," It is cold", and " It is pleasant," respectively. Then the statement "It is not raining and it is pleasant, and it is not pleasant only if it is raining and it is cold" is represented byQ200.
Consider the sequence \left \langle x_n \right \rangle,\; n \geq 0 defined by the recurrence relation x_{n + 1} = c \cdot (x_n)^2 - 2, where c > 0. For which of the following values of c, does there exist a non-empty open interval (a, b) such that the sequence x_n converges for all x_0 satisfying a < x_0 < b? i. 0.25 ii. 0.35 iii. 0.45 iv. 0.5