Notes, summaries, assignments, exams, and problems for Other languages

Present Simple Tense

Affirmative

• I, You, We, They + verb (e.g., I work, You work, We work, They work) - Without 's' or 'es' at the end of the verb.
• He, She, It + verb + s/es (e.g., He works, She works, It works) - With 's' or 'es' at the end of the verb.

Negative

• I, You, We, They + don't + verb (e.g., I don't work)
• He, She, It + doesn't + verb (e.g., He doesn't work) - No 's' or 'es' is added to the main verb because 'doesn't' already includes it.

Time Expressions

• Always
• Every (day, week, month, year...)
• Once (a day, a week...)
• Twice (a day, a week...)
• Never
• Normally
• Often
• Seldom
• Sometimes
• Usually
• Generally
• Rarely

Present Continuous Tense

Affirmative

• I + am + verb + -ing (e.g., I'm working)
• You, We, They + are + verb + -ing (e.g., You are working, We are working,

Probability Distributions

Types of Probability Distributions

Normal Distribution

• Used to model continuous data
• Examples: Heights of people, scientific measurements, test scores

Binomial Distribution

• Used to model discrete data with two possible outcomes
• Examples: Number of heads in a coin toss, number of successes in a series of trials

Poisson Distribution

• Used to model the number of events occurring in a fixed interval of time or space
• Examples: Number of phone calls received per hour, number of earthquakes per year

Applications of Probability Distributions

• Sales success
• Launch of new products
• Bidding for contracts
• Quality control
• Hiring staff
• Experimental trials

Calculating Probabilities

Normal Distribution

• Use a calculator or statistical software
• Formula: P(

Fundamentals of Logic and Reasoning

What is Logic?

Logic is the philosophical discipline that studies the correctness or validity of our reasoning.

The Role of Language in Argumentation

By means of language, we perform various actions: begging someone to lend us money, asking for directions, describing our home, or even, if you have sufficient authority, issuing a command like throwing someone in jail.

Structure of Reasoning, Arguments, and Inferences

A valid argument or inference consists of two main components:

1. Premises: A set of statements expressing the input data or evidence.
2. Conclusion: The final statement expressing new information obtained directly from the premises.

Example of Deductive Reasoning

• Premise 1: The cheese thief is a cat or a mouse.

Relative Clauses in Catalan Grammar

Relative pronouns introduce subordinate clauses. They relate to a substantive element and its antecedent. Examples include: who (el qui parla francès que ens ajudi), when (quan cantaves encara no plovia), how (voldreu pintar l'habitació com...), and where (on es troba on Crist va perdre...) with a relative antecedent.

Specificative Relatives

These are used without a preposition: that (que he vist en la pel·lícula val molt), how (m'agrada la manera com ho veus), or where (el país on sé que no plou). With a preposition: where (en què la moral i reflexions molt antigues són), who (la parella que ha vingut amb qui balles sempre), which (fa un pa del qual l'aroma m'és sensacional), or where (la conversa

Spanish-English Vocabulary: Set 1

• 1) Tener, poseer: to own, to possess.
• Humanidad: humanity, mankind.
• Dejar de: to give up, to stop.
• Junto con: along with, together with.
• Accurate: precise.
• Pasarlo bien: to have a good time; to enjoy oneself.
• Travieso: naughty, mischievous.
• También: as well, too.
• Range: variety.
• Estar parado: to be unemployed; to be out of work.
• Reconfortante: comforting, reassuring.
• Anticuado: out of date, unfashionable.
• Como si: as if, as though.
• Increíble: incredible.
• To be upset: annoyed, angry.
• Fijarse en: to spot, to notice.
• Resultar ser: to prove; to turn out to be.
• Wealthy: well off, rich.
• 2FILA: Whether: characteristic.
• Actually: in fact, really.
• To worship: to adore.
• Sobresaliente: remarkable, outstanding.
• Últimamente: recently, lately.