3. We want to find S so ((A = B) A B) = S is a tautology. A B (A=B) A B TT ((A = B) ^ B) = S S TF FT FF (a) Explain why S can't be A. (b) Explain why S can't be ¬A. (c) Find S that makes a tautology. (d) Explain why, in this case, the statement S isn't useful. (If y wrote out simple statements A and B, the answer to this questi is obvious),
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A statement is a sentence that can either be true or can be false but not both at the same time. But not every sentence can be a statement. There are some rules that a sentence has to follow in order to be considered a statement.
A sentence will not be a statement if:
- It is an exclamation.
- It is an order or request.
- It is a question.
- It contains variable time.
- It contains variable places.
- It contains pronouns.
A simple statement is a statement that cannot be broken into multiple statements.
A compound statement is a statement containing two or more simple statements.
We use connectives to join two or more statements to form a compound statement.
There are three basic connectives used:
- Conjunction: It corresponds to the word 'and'.
- Disjunction: It corresponds to the word 'or'.
- Negation: It corresponds to the word 'not'.
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