LESSON 2.1 Propositions Flashcards
What is a proposition in mathematics?
A proposition is a declarative sentence that can be objectively identified as either true or false, but not both.
How do we denote the truth values of a proposition?
If a proposition is true, its truth value is denoted by T or 1. If false, it is denoted by F or 0.
Is the sentence “Douglas MacArthur arrived in the Philippines in 1521” a proposition? What is its truth value?
Yes, this sentence is a proposition because it can be objectively true or false. Its truth value is false, as historical records show that Douglas MacArthur arrived in the Philippines in the 1900s, not 1521.
Is the sentence “Are you insane?” a proposition? Why or why not?
No, this sentence is not a proposition because it is a question, not a declarative sentence. Propositions must be statements that can be objectively evaluated as true or false.
Is the sentence “√2 is an irrational number” a proposition? What is its truth value?
Yes, this sentence is a proposition because it is a declarative sentence that can be identified as true or false. Its truth value is true, as √2 is indeed an irrational number.
Is the sentence “Find all x such that xe^(-x) = 2” a proposition? Why or why not?
No, this sentence is not a proposition because it is a command or an instruction. A proposition must be a declarative sentence that can be judged as true or false.
Is the sentence “Is that your laptop?” a proposition? Why or why not?
No, this sentence is not a proposition because it is a question. Propositions must be declarative sentences that can be evaluated as true or false.
Is the sentence “Basketball players are handsome” a proposition? Why or why not?
No, this sentence is not considered a proposition because “handsome” is subjective and open to personal interpretation. Propositions require an objective truth value, which this sentence lacks due to its subjectivity.
Is the sentence “There is life on other planets” a proposition? Can we assign a truth value to it?
Yes, this sentence is a proposition because it can be either true or false. However, we cannot currently assign a truth value, as there is no definitive evidence confirming or denying the existence of life on other planets.
Is the sentence “Welcome to the Philippines!” a proposition? Why or why not?
No, this sentence is not a proposition because it is an exclamation, not a declarative sentence. Propositions must state something that can be objectively true or false.
What is the negation of a proposition?
The negation of a proposition p is a proposition that is false when p is true, and true when p is false. It is denoted by ¬ p.
How can negation be expressed in the English language?
In English, we can express the negation of a proposition p by stating, “It is not the case that p,” or by grammatically modifying the sentence, such as replacing “is/are” with “is not/are not.”
What is the negation of the statement “Everyone in Visayas speaks Cebuano”?
The negation of this statement is: “Not everyone in Visayas speaks Cebuano.”
