Recent questions tagged propositional-logic

During the most recent fiscal year, Acme Computer had an annual revenue of \$138 billion and a net profit of \$8 billion, Nadir Software had an annual revenue of \$87 bil...

Given: Acme Computer (revenue \$138B, profit \$8B), Nadir Software (revenue \$87B, profit \$5B), Quixote Media (revenue \$111B, profit \$13B). Which of the following prop...

Smartphone A has 256 MB RAM and 32 GB ROM with an 8 MP camera. Smartphone B has 288 MB RAM and 64 GB ROM with a 4 MP camera. Smartphone C has 128 MB RAM and 32 GB ROM wit...

Given: Smartphone A (256 MB RAM, 32 GB ROM, 8 MP), Smartphone B (288 MB RAM, 64 GB ROM, 4 MP ), Smartphone C ( 128 MB RAM, 32 GB ROM, 5 MP ). Which of the following propo...

Let $\mathrm{S}=$ "I study for this exam", $\mathrm{A}=$ "I attend class", $\mathrm{P}=$ "I pass the class." The statement "If I study for this exam and attend class, the...

Let $P, Q,$ and $R$ be three atomic propositional assertions. Let $X$ denote $( P ∨ Q ) → R$ and $Y$ denote $(P → R) ∨ (Q → R).$ Which one of the following is a tautology...

Which of the following is the correct negation of the statement "There exists a living person who is 150 years old"?There exists a living person who is not 150 years old....

Which of the following is the correct negation of the statement "For all positive integers n, $\mathrm{n}+2>8^{\prime \prime}$ ?For all positive integers $n, n+2 \leqslan...

A formula of the form $\mathrm{P} \rightarrow \mathrm{Q}$ is said to be valid (a tautology) when its antecedent P is always FALSE - this is called a vacuous truth. In the...

Let $\mathrm{p}=$ "It is below freezing" and $\mathrm{q}=$ "It is snowing." Which of the following correctly translates: "That it is below freezing is necessary and suffi...

Let p = "It is below freezing" and q = "It is snowing." Which of the following correctly translates: "Either it is below freezing or it is snowing, but it is not snowing ...

In the proof of $\neg(p \vee(\neg p \wedge q)) \equiv \neg p \wedge \neg q$, which law justifies the step:$$\neg p \wedge(p \vee \neg q) \equiv(\neg p \wedge p) \vee(\neg...

Which sequence of laws correctly proves $\mathrm{p} \vee(\mathrm{p} \wedge \mathrm{q}) \vee(\neg \mathrm{p} \wedge \mathrm{r}) \equiv \mathrm{p} \vee \mathrm{r}$ ?Distrib...

Consider the two formulas:$$\begin{aligned}& \mathrm{F} 1=(\mathrm{p} \wedge \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{q} \wedge \mathrm{r}) \\& \mathrm{F} 2=(\mathrm{p}...

$$\neg \mathrm{I} \rightarrow \neg \mathrm{C}, \mathrm{D} \rightarrow \mathrm{~S}, \neg \mathrm{P} \rightarrow \neg \mathrm{D}, \neg \mathrm{~S} \vee \mathrm{I}, \mathrm{...

Consider the statement: "Students cannot skype during the test unless the internet is on."Let $\mathrm{I}=$ "the internet is on" and $\mathrm{S}=$ "students can skype dur...

Julie and Jamie are identical twins - one always lies and one always tells the truth. You meet one of them but do not know which twin lies. You ask the 3-word question "D...

Given $P=T, Q=T, R=F, S=F$, find the truth value of:$$(\mathrm{P} \vee(\mathrm{Q} \rightarrow(\mathrm{R} \wedge \neg \mathrm{P}))) \leftrightarrow(\mathrm{Q} \vee \neg \m...

Given $P=T, Q=T, R=F, S=F$, what is the truth value of $(P \leftrightarrow R) \wedge(\neg Q \rightarrow S)$ ?TRUE, because both conjuncts are TRUE.FALSE, because $\mathrm...

Given $P=T, Q=T, R=F, S=F$, find the truth value of:$$\neg(\mathrm{P} \wedge \mathrm{Q}) \vee \neg \mathrm{R}) \vee((\mathrm{Q} \leftrightarrow \neg \mathrm{P}) \rightarr...

Consider the statement: "Every Eulerian graph is connected." Which of the following pairs correctly states the converse and inverse of this implication?Converse: Every co...

Consider the implication: " $\mathrm{ab}=0 \rightarrow \mathrm{a}=0$ or $\mathrm{b}=0$." Which of the following is the inverse of this statement?If $\mathrm{a}=0$ or $\ma...

Consider the implication: "If $\mathrm{a} / \mathrm{b}$ and $\mathrm{b} / \mathrm{c}$ are integers, then $\mathrm{a} / \mathrm{c}$ is an integer." Which of the following ...

If a propositional formula has 5 variables, how many rows are needed in its truth table?

The simplified Boolean expression for the given network. $\mathrm{p} \wedge \mathrm{q} \wedge \mathrm{t}$$\mathrm{p} \wedge(\mathrm{q} \vee(\mathrm{r} \wedge \mathrm{t}))...

What is the simplified Boolean expression for given network?$\neg \mathrm{q} \vee(\mathrm{p} \wedge \neg \mathrm{r})$$\mathrm{p} \wedge \neg \mathrm{q}$$\mathrm{p} \vee \...

Two restaurants display the following signs:Restaurant 1: "Good food is not cheap."Restaurant 2: "Cheap food is not good."$g=$ "The food is good" and $c=$ "The food is ch...

There are two troll tribes - Glums (always tell truth) and Plogs (always lie). You meet two trolls, Kim and Coin:Kim says: "We are from different clans."Coin says: "Kim i...

A tennis magazine advertisement states:"IfI'm not playing tennis, I'm watching tennis. And if I'm not watching tennis, I'm reading about tennis."The speaker can only do o...

$p=$ "It is raining", $q=$ "I have a headache", $r=$ "I attend the lecture"The statement $S$ : "If it is not raining and I do not have a headache, then I attend the lectu...