Mathematics from zero
True and false
A light switch is either on or off — never half. Logic treats sentences the same way. A sentence like “5 is greater than 3” is simply on: true. “2 plus 2 equals 5” is simply off: false. No in-between.
After this lesson you can say what a statement is, tell a statement apart from a sentence that is not one, and give the truth value of a statement.
A statement is a sentence that is definitely true or definitely false. “5 is greater than 3” is a statement — and it is true. “2 plus 2 equals 5” is also a statement — and it is false. What makes both of them statements is that each one lands firmly on one side: true, or false.
Not every sentence is a statement. “What time is it?” is a question — it is neither true nor false. “Close the door” is a command — also neither. “This soup is tasty” is an opinion — it has no fixed answer everyone must agree on. Only sentences that are definitely true or definitely false count as statements in logic.
Every statement has one truth value: true or false. The truth value of a
statement is which of the two it is. It is helpful to write these as numbers: 1 for
true, 0 for false — like the switch being on or off. Every statement carries exactly
one of these, and never both.
The truth value is fixed — that is what makes logic possible. Because “5 > 3” is true and stays true, you can build longer reasoning on top of it without the ground shifting. Logic is the study of combining statements; it only works because each statement holds still at one truth value. The next lesson combines them.
Decide which of these are statements, and give the truth value of each one that is.
“7 is greater than 2” — this is definitely true. It is a statement, truth value true
(1).
“4 equals 5” — this is definitely false. It is a statement, truth value false (0).
“Please sit down” — this is a command. It is not true or false, so it is not a statement at all.
“Is it raining?” — this is a question. Again not true or false, so not a statement.
Two of the four are statements; the other two are simply not the kind of sentence logic works with.
Why this works
Why does logic refuse questions, commands, and opinions? Because logic’s job is to combine facts reliably, and that needs each piece to have a definite, unchanging answer. A question has no answer to combine; an opinion’s answer changes from person to person. Only a sentence pinned to true or false gives logic something solid to build with.
Common mistake
A common mistake is thinking a statement has to be true to count as a statement. It does not. “2 + 2 = 5” is a perfectly good statement — it just has the truth value false. A statement only needs to be definitely true or definitely false. Being false does not disqualify it.
Is the statement '7 > 2' true? Type 1 for true, 0 for false.
Is the statement '4 = 5' true? Type 1 for true, 0 for false.
Is the statement '3 + 3 = 6' true? Type 1 for true, 0 for false.
A statement is true. Written as a number, what is its truth value?
Is the statement '10 < 9' true? Type 1 for true, 0 for false.
Which sentence is a statement in the logical sense?
A statement is a sentence that is definitely true or definitely false. Questions, commands, and opinions are not statements — they have no fixed truth value. Every statement has exactly one truth value, true or false, often written as 1 or 0. That truth value is fixed, and that fixedness is what lets logic build reliable reasoning out of statements.