Thinking Mathematically Logic 3.1 Statements, Negations, and Quantified Statements.

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Thinking Mathematically Logic 3.1 Statements, Negations, and Quantified Statements

Statements A “statement” is a sentence that is either “true” or “false” but not both at the same time. Exercise Set 3.1 #3, 9 Statement?  On January 20, 2009, John McCain became America’s 44 th president.  Is the unexamined life worth living?  = 16.

Statements - “Negation” The “negation” of a statement is another statement that has the opposite “truth value.” That is when a statement is true its negation is false and when the statement is false its negation is true. Exercise Set 3.1 #15 Form the negation of “It is raining” What is the negation of 2+2 = 5

Statements - “Symbolism” Just as x can be used as a name for a number, a symbol such as p can be used as a name for a statement. When p is used as a name for a statement the symbols ~p are used as a name for the negation of p.

Examples: Using Symbols for Statements Exercise Set 3.1 #23 p: One works hard q: One succeeds r: The temperature outside is not freezing s: It is not true that the heater is working The temperature outside is freezing = ? Exercise Set 3.1 #27 p: Listening to classical music makes infants smarter. q: Subliminal advertising makes you buy things. r: Sigmund Freund’s father was not 20 years older than his mother. s: Humans and bananas do not share approximately 60% of the same DNA structure. ~r = ?

“Quantified” Statements A “quantified” statement is one that says something about “all”, “some”, or “none” of the objects in a collection. Exercise Set 3.1 #29, #31, #35 For each of the statements:  All whales are mammals.  Some students are business majors.  No Democratic presidents have been impeached. Give an equivalent statement Negate the statement.

Thinking Mathematically Logic 3.1 Statements, Negations, and Quantified Statements