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Questions and Answers
Which of the following statements is a proposition?
Which of the following statements is a proposition?
- My seatmate will get a perfect score in the Logic exam. (correct)
- Find a number which divides your age.
- Mindanao is an island in the Philippines.
- Welcome to the Philippines.
Which of the following statements is not a proposition?
Which of the following statements is not a proposition?
- $3 + 2 = 5$
- What is the domain of the function. (correct)
- $f(x) = x/(x+1)$ is a rational function.
- $2x + 1 = 3$
From the given symbolic propositions, which one is false?
From the given symbolic propositions, which one is false?
- $\pi \notin \mathbb{Q}$ (correct)
- $2 \in \mathbb{N}$
- $-100 \in \mathbb{Z}$
- $\pi \in \mathbb{R}$
Express the conjunction $p \land q$ as an English sentence.
Express the conjunction $p \land q$ as an English sentence.
Which of the following statements is equivalent to $p \land (\sim q)$?
Which of the following statements is equivalent to $p \land (\sim q)$?
Which of the following symbols best represents the conjunction of two propositions?
Which of the following symbols best represents the conjunction of two propositions?
Which symbol is used to denote the disjunction operator?
Which symbol is used to denote the disjunction operator?
In the context of logic, what is a disjunction?
In the context of logic, what is a disjunction?
What does the proposition 𝑝 ∨ (𝑞 ∨ 𝑟) translate to in English?
What does the proposition 𝑝 ∨ (𝑞 ∨ 𝑟) translate to in English?
What is the truth value of the proposition ( ∼ 𝒑) ∨ (𝒒 ∧ 𝒓) if 𝒑 is false, 𝒒 is true, and 𝒓 is false?
What is the truth value of the proposition ( ∼ 𝒑) ∨ (𝒒 ∧ 𝒓) if 𝒑 is false, 𝒒 is true, and 𝒓 is false?
What does the conditional 𝑝 → 𝑞 represent?
What does the conditional 𝑝 → 𝑞 represent?
How is the truth value of a conditional proposition 𝑝 → 𝑞 defined?
How is the truth value of a conditional proposition 𝑝 → 𝑞 defined?
What does the conditional proposition 𝑝 → 𝑞 imply?
What does the conditional proposition 𝑝 → 𝑞 imply?
Which symbol is used to denote the conditional operator?
Which symbol is used to denote the conditional operator?
If the hypothesis of a conditional proposition is false, what can be said about the truth value of the conclusion?
If the hypothesis of a conditional proposition is false, what can be said about the truth value of the conclusion?
"Either Victor has a date with Liza or Janree is sleeping, or Eumir is eating." translates to which disjunction in symbols?
"Either Victor has a date with Liza or Janree is sleeping, or Eumir is eating." translates to which disjunction in symbols?
"Either Victor has a date with Liza, or Janree is sleeping and Eumir is eating." translates to which disjunction in symbols?
"Either Victor has a date with Liza, or Janree is sleeping and Eumir is eating." translates to which disjunction in symbols?
Study Notes
Propositions
- A proposition is a statement that can be either true or false.
- Example of a proposition: statements that can be classified as true or false.
- Example of a non-proposition: questions, commands, or exclamations.
Conjunction
- The conjunction of two propositions is represented by the symbol ∧.
- The conjunction p ∧ q translates to "p and q" in English.
- Example: equivalent to p ∧ (∼q) is "p is true, but q is false".
Disjunction
- The disjunction operator is represented by the symbol ∨.
- A disjunction is a statement that is true if at least one of the propositions is true.
- The proposition p ∨ (q ∨ r) translates to "p or q or r" in English.
- Example: "Either Victor has a date with Liza or Janree is sleeping, or Eumir is eating." translates to p ∨ (q ∨ r).
Conditional
- The conditional operator is represented by the symbol →.
- The conditional p → q represents "if p, then q".
- The truth value of a conditional proposition p → q is defined as:
- If p is true and q is true, then p → q is true.
- If p is true and q is false, then p → q is false.
- If p is false, then p → q is true regardless of q.
- A conditional proposition p → q implies that if p is true, then q must be true.
- If the hypothesis of a conditional proposition is false, the truth value of the conclusion is true.
Translations
- "Either Victor has a date with Liza, or Janree is sleeping and Eumir is eating." translates to p ∨ (q ∧ r).
- "Either Victor has a date with Liza or Janree is sleeping, or Eumir is eating." translates to p ∨ (q ∨ r).
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Description
Test your knowledge about propositions in logic with this quiz. Learn about the basic principles and characteristics of propositions and their truth values.
