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1.2 Symbolic Logic! (Hooray!)
Statements vs. Non­statements
A "statement" is a sentence that can be either true or false or both.
MJC is a community college.
MJC is located in Hawaii.
This statement is false.
MJC is the best community college.
Are you a student?
The year is 2013.
This statement is true.
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Negation ("opposite")
Easy cases: Yes/No type statements
p = a snake is a mammal.
~p = a snake is NOT a mammal.
Trickier: Quantity relations
q = all snakes have forked tongues
~q = SOME snakes do NOT have forked tongues
r = no snakes have legs
~r = SOME snakes DO have legs
Please note: "All" and "No" are NOT opposites!
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Conjunction
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("and")
p = I passed Astronomy
q = I passed History
p∧q = I passed both Astronomy AND History
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Disjunction
("or")
p = I am a student
q = I am an employee
p∨q = I am a student OR an employee
In English, "or" has two different meanings. Sometimes it means you can't have both, and sometimes both is acceptable. In math, we use the more inclusive meaning.
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Conditional
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("If ... then")
p = it is raining
q = I bring an umbrella
p⇒q = If it is raining, then I bring an umbrella
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Alternative Wordings of If ... Then
No "then" ­ "If it is raining, I will drive to work."
Backwards ­ "I'll work on Saturday if you pay me."
Double Backwards ­ "I'll work on Saturday only if you pay me."
Necessary and Sufficient
"Coffee is sufficient for waking up in the morning."
"Taking the final is necessary for passing my class."
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Quiz #1
Of the following three choices, which chapter should be included in this class?
a) Chapter 2 (Sets, Counting, and Infinity)
b) Chapter 7 (Number Systems and Number Theory)
c) Chapter 8 (Geometry)
d) Chapter 13 (Calculus)
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