Recent questions tagged mathematical-logic

​​​Let $P(x)$ be an arbitrary predicate over the domain of natural numbers. Which ONE of the following statements is TRUE?$\big (P(0) \wedge \big( \forall x [P(x) \Righta...

​​​​​​If $P \: e^{x} = Q \: e^{-x}$ for all real values of $x$, which one of the following statements is true?$P = Q = 0$$P = Q = 1$$P = 1; Q = -1$$\frac{P}{Q} = 0$ 

Which of the following predicate logic formulae/formula is/are CORRECT representation(s) of the statement: "Everyone has exactly one mother"?The meanings of the predicate...

Select the statement that is the negation of "Some weasels are cuddly."No weasels are cuddly.All weasels are cuddly.Some weasels are not cuddly.All cuttlefish are weasely...

We use the dictionary:\begin{array}{ll}M & \text{domain of men} \\s & \text{Sharon} \\N(x) & \text{x is nice} \\L(x, y) & \text{x loves y}\end{array}Which of the followin...

Consider the following two logical equivalences that express 'logical laws':$\mathrm{\neg \forall_{x \in D} f \equiv \exists_{x \in D}\neg f}$$\neg(f \leftrightarrow g) \...

Consider the sentence:Nadhi eats a fruit only if the fruit is an apple.Define the propositional variables:$n$ : Nadhi eats a fruit.$a$ : The fruit is an apple.Which of th...

Let $\operatorname{Bird}(x)$ means " $x$ is a $\operatorname{bird}$" and $\mathrm{Fly(y)}$ means " $y$ can fly". Which of the following is a correct logical statement for...

Consider the following interpretation of a language with a unary predicates $P, Q$, and a binary predicate $R$.Universe $=\{1,2,3,4\}$$P=\{\langle 1\rangle,\langle 3\rang...

Suppose the marked diagram below conveys information about relationships between pirates, ruffians and scoundrels. We use shading to indicate that a region contains no el...

The statement form $(p \Leftrightarrow r) \Rightarrow(q \Leftrightarrow r)$ is equivalent to$[(\sim p \vee r) \wedge(p \vee \sim r)] \vee \sim[(\sim q \vee r) \wedge(q \v...

Which of the following formulas is a formalization of the sentence:"Every connected and circuit-free graph is a tree"Where $\operatorname{cir}(\mathrm{x})$ means " x has ...

Given the statement form below where $p, q, r, s$ are statement variables,$$\Biggl(\biggl(\Bigl((p \rightarrow q) \rightarrow(q \rightarrow r)\Bigl) \rightarrow(r \righta...

The island of Wantuutrewan is inhabited by exactly two types of natives: knights who always tell the truth and knaves who always lie. Every native is a knight or a knave,...

Given the following where $p, q, r, s, t$ are statement variables:(i) $(\sim r \rightarrow \sim r) \vee(\sim q \rightarrow q) \vee(t \rightarrow \sim t)$(ii) $(p \wedge q...