Answer to Question #250307 in Discrete Mathematics for Toby

Question

Which of the following are propositions? Of those which aren’t, explain why.

The baby is laughing.

What’s that noise?

1 + 1 = 3

Get out of here!

He ran in the race but slipped on a banana peel.

What a glorious day it is!

Santa Claus is jolly.

To fail to achieve the impossible is not to fail.

Please pay attention.

All triangles have four sides.

The next Prime Minister will be a woman.

What are you thinking?

If it rains then there is moisture in the air.

I wish to be immortal.

Neither circumstances nor criticism will prevent my progress.

Won’t you close the door?

Santa Claus is a fictional character.

Let x mark the spot.

Your wish is my command.

Define ‘proposition’ to mean ‘bearer of one truth’.

Answer 1

The baby is laughing. – a proposition

What’s that noise? – not a proposition (because this is a question and can neither be false nor true)

1 + 1 = 3 – a proposition

Get out of here! - Not proposition (because this is not a declarative statement that can be either a false or true statement)

He ran in the race but slipped on a banana peel. – a proposition

What a glorious day it is! – not a proposition (because this is not a declarative statement that can be either a false or true statement)

Santa Claus is jolly. - a proposition

To fail to achieve the impossible is not to fail. - a proposition

Please pay attention. – not a proposition (because this is not a declarative statement that can be either a false or true statement)

All triangles have four sides. – a proposition

The next Prime Minister will be a woman. – a proposition

What are you thinking? – not a proposition (because this is a question and can neither be false nor true)

If it rains then there is moisture in the air. - a proposition

I wish to be immortal. – not a proposition (because this is not a declarative statement that can be either a false or true statement)

Neither circumstances nor criticism will prevent my progress. – a proposition

Won’t you close the door? – not a proposition (because this is a question and can neither be false nor true)

Santa Claus is a fictional character. - a proposition

Let x mark the spot. – not a proposition (because this is not a declarative statement that can be either a false or true statement)

Your wish is my command. – a proposition

Define ‘proposition’ to mean ‘bearer of one truth’.  

Proposition is a meaningful declarative statement and all and only meaningful-declarative-sentences are propositions