Which of these are propositions? What are the truth values...

Which of these are propositions? What are the truth values of those that are propositions?
a) Do not pass go.
b) What time is it?
c) There are no black flies in Maine.
d) $4+x=5$.
e) The moon is made of green cheese.
f) $2^{n} \geq 100$.

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Key Concepts

Proposition

A proposition is a declarative sentence that is definitively either true or false. It is a fundamental concept in logic and forms the basis for reasoning and argumentation. This means that the statement must clearly assert a fact or claim that can be evaluated objectively, without ambiguity or context dependency.

Truth Value

The truth value of a proposition is the attribute that assigns to it a designation of either being true or false. In classical logic, every proposition must have one of these truth values, and this concept is essential for performing logical analysis and constructing valid arguments.

Open Sentence

An open sentence, also known as a predicate or propositional function, is a statement that contains one or more free variables and does not have a truth value until those variables are instantiated. In logical analysis, distinguishing between propositions (which have a fixed truth value) and open sentences is crucial for understanding and constructing logical expressions.

Transcript

00:01 Okay, we've got a fun question here.

00:02 Which of these are propositions? and what are the truth values of those propositions? so what's a proposition? a proposition is a statement that is either true or false.

00:25 Okay, the sky is blue.

00:27 That's a proposition because it's either true or false.

00:31 So we're going to go through these and we are going to see what we can do.

00:38 Alright, so this first one here, do not pass go, that is a command, right? monopoly, the game monopoly, i believe.

00:50 It's a command and so it's not true or false, so it is not a proposition.

00:57 A proposition, okay? that one was fun.

01:09 Let's try the next one.

01:10 What what time is it? what time is it? i don't know.

01:13 It's 1 .20 here.

01:14 What time is it? that's a question.

01:16 It is not a, so the first one was a command.

01:22 Do not pass go.