Propositional Logic
Q31.
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))?Q32.
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 preciousQ33.
Which of the following is the negation of [\forall x, \alpha \rightarrow(\exists y, \beta \rightarrow(\forall u, \exists v, y))]Q34.
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 automatonQ35.
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?Q36.
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.Q37.
P and Q are two propositions. Which of the following logical expressions are equivalent? I. P\vee \sim Q II.\sim (\sim P \wedge Q) III.(P \wedge Q)\vee (P\wedge \sim Q)\vee (\sim P\wedge \sim Q) IV. (P\wedge Q)\vee \vee (P\wedge \sim Q)\vee (\sim P\wedge Q)Q38.
Identify the correct translation into logical notation of the following assertion. Some boys in the class are taller than all the girls Note: taller (x, y) is true if x is taller than y.Q39.
Consider the following first order logic formula in which R is a binary relation symbol. \forall x \forall y(R(x, y) \Longrightarrow R(y, x)),The formula isQ40.
Let P(x) and Q(x) be arbitrary predicates. Which of the following statements is always TRUE?