statement

<2023-04-01 Sat 17:51:39> mahmood

math

a proposition is a declarative statement that may be either true or false but never both.
[cite:@kohavi_switching_2010 chapter 3.3 isomorphic systems]

to prove that a property exists for every statement, we prove that

the property exists for every boolean variable
if the property exists for statement $\text{[math]}$ then it also exists for $\text{[math]}$
if the property exists for the statements $\text{[math]}$ and $\text{[math]}$ then it also exists for $\text{[math]}$

to represent a statement using a binary tree

if the statement $\text{[math]}$ is a boolean variable, draw a single node for $\text{[math]}$

examples of sentences that are (or make) true statements:

"Socrates is a man."
"a triangle has three sides."
"madrid is the capital of Spain."