EECS 203-1: Discrete Mathematics Winter 2005 Introductory ...
EECS 203-1: Discrete Mathematics Winter 2005 Introductory ... EECS 203-1: Discrete Mathematics Winter 2005 Introductory ...
Propositions • A proposition is a declarative statement that has a definite truth content: either true or false. • Examples: (i) Toronto is the capital of Canada. (ii) 2 + 2 = 3. (iii) Kevin Bacon is the Pope. (iv) Saddam is the new U of M assistant defensive coordinator. • Non- propositions: (i) What time is it (ii) x + 1 = 4. (iii) He is the Pope. • Sometimes you have contextual information that tells you what x’s value is, or who ”he” is. Then statements like (ii) and (iii) are propositions, but only relative to a context or situation. • A statement like x + x = 2x is technically not a proposition, even though it’s true for all numbers x. 4
Compound propositions • These are propositions that are built out of other ones, starting with basic ones, using logical operators, also called propositional connectives or Boolean connectives. • We start with a simple operator called negation. Definition Let p be a proposition. The statement “It is not the case that p” is called the negation of p, and is denoted by ¬p, and read “not p”. Example (i) (Relative to Jan. 7, 2005) Let p be “Today is Tuesday”. Then ¬p is “It is not the case that today is Tuesday”, or “today is not Tuesday”, or “it is not Tuesday today”, (ii) Let p be “1 + 1 = 2” Then ¬p is “1 + 1 ≠ 2”. 5
- Page 1 and 2: EECS 203-1: Discrete Mathematics Wi
- Page 3: Part I: Logic (Text section 1.1)
- Page 7 and 8: Still more operators • The exclus
- Page 9 and 10: Complex expressions in propositiona
Propositions<br />
• A proposition is a declarative statement that has a definite truth content:<br />
either true or false.<br />
• Examples: (i) Toronto is the capital of Canada. (ii) 2 + 2 = 3. (iii) Kevin<br />
Bacon is the Pope. (iv) Saddam is the new U of M assistant defensive<br />
coordinator.<br />
• Non- propositions: (i) What time is it (ii) x + 1 = 4. (iii) He is the Pope.<br />
• Sometimes you have contextual information that tells you what x’s value<br />
is, or who ”he” is. Then statements like (ii) and (iii) are propositions, but<br />
only relative to a context or situation.<br />
• A statement like x + x = 2x is technically not a proposition, even though<br />
it’s true for all numbers x.<br />
4
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