Chapter 2: Sets and Logic - Simple and Compound Propositions

Question-and-answer flashcards covering propositions, simple vs. compound statements, connectives, negation, translation between English and symbolic form, truth tables, and DeMorgan’s laws.

What is a proposition?

A declarative sentence that is either true or false, or asserts something that is true or false.

What is a simple statement?

A statement that conveys a single idea.

What is a compound statement?

A statement that conveys two or more ideas, formed by connecting simple statements with words such as and, or, if … then, or if and only if.

What is a connective?

A word or phrase that connects simple statements to form a compound statement (e.g., and, or, if … then, if and only if).

Is 'Florida is a state in the United States' a proposition?

Yes. It is a declarative sentence that is true, hence a proposition.

Is 'How are you?' a proposition?

No. It is a question, not a declarative proposition.

Is 'Humans cause climate change' a proposition?

Yes. It is a declarative proposition asserting a truth value.

Is '10,001 is a prime number' a proposition?

Yes. It is a declarative statement that is either true or false.

Is 'Run for cover' a proposition?

No. It is a command, not a proposition.

Is 'This sentence is false' a proposition?

No. It creates a paradox: assuming true implies false and vice versa, so it is not a proposition.

Negation of 'Soccer is a team sport'

Soccer is not a team sport.

Negation of 'The dog does not need to be fed'

The dog needs to be fed.

Translate p ∧ q to English, given p: Today is Friday; q: It is raining

Today is Friday and it is raining.

Translate ∼r ∨ q to English, given r: I am going to a movie; q: It is raining

I am not going to a movie or it is raining.

Translate p → q to English, given p: Today is Friday; q: It is raining

If today is Friday, then it is raining.

What is the truth value of p ∧ q?

True only when both p and q are true; otherwise false.

State De Morgan's laws for propositions

¬(p ∨ q) ≡ (¬p) ∧ (¬q) and ¬(p ∧ q) ≡ (¬p) ∨ (¬q).

What is a truth table?

A table showing the truth-values of a compound statement for all possible truth-values of its simple statements.

Express an irrational number using DeMorgan’s law, given p = 'terminating decimal' and q = 'repeating decimal'

An irrational number satisfies ¬(p ∨ q) ≡ (¬p) ∧ (¬q): not terminating and not repeating.