Truth Value
A True/False game of logical statements
A True/False game of logical statements
A statement is a declarative sentence that is true or false. This value is called the statement's truth value.
We can connect statements with phrases like "and", "or", "if... then", etc. to create a compound statement. A statement that is not a compound statement is a simple statement.
This game is designed to teach and test you on truth value basics.
For each problem in this game, you will be shown a statement. All you have to do is click on the correct truth value below it. Give it a try.
The sun is a star.
We can change a statement's truth value to create a new statement. For instance we can precede the statement with "It is not the case that" (or a similar phrase). Example:
"Earth is a planet."(A true statement.)
"It is not the case that Earth is a planet."(A false statement.)
If we combine two statements with "and" (or "plus" or "but", etc.) then the new statement will only be true when both of the original statements were true. Example:
"Earth is a planet and the sun is a star."(A true statement.)
"Earth is a planet and the sun is an asteroid."(A false statement, since at least one of the starting statements is false.)
If we combine two statements with "or" then the new statement will only be false when both of the original statements were false. Example:
"Earth is a planet or the sun is an asteroid."(A true statement, since at least one starting statement is true.)
"Earth is a galaxy or the sun is an asteroid."(A false statement, since both of the starting statements are false.)
If we combine two statements with "if [[the first statement]] then [[the second statement]]" then the new statement will only be false when the first statement was true but the second statement was false. Example:
"If the sun is an asteroid then I'm the Queen of Mesopotamia."(A true statement, since both starting statements are false.)
"If the sun is a star then I'm the Queen of Mesopotamia."(A false statement, since the "if" statement is true, but the "then" statement is false.)
If we combine two statements with "if and only if" then the new statement will only be true when both of the original statements had the same truth value (both true, or both false). Example:
"Earth is a planet if and only if the sun is a star."(A true statement.)
"Earth is a galaxy if and only if the sun is an asteroid."(Also a true statement.)
"Earth is a galaxy if and only if the sun is a star."(A false statement, since the starting statements had different truth values)