Lecture 2.doc

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9 Apr 2012
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Claims (True or False) have form:
Certain things have certain properties/
1. Every employee makes less than 70,000
True or False? True
How. Check whether or not claim is true for every employee.
Words.
Every, Each, All.
Indicate universal (claim refers to every object of domain) quantification
(connecting prop. Of elements to prop. Of set)
2. Each employee makes less than 70,000
3. All employees make less than 70,000
In logic:
UQ(universal quantification) refers to every object in domain.
In English:
Every January it shows in Toronto
(consider true thought acknowledge does not always hold)
Claim
4. Each employee makes atleast 10,000.
A false claim. Since betty makes under 10,000.
Betty is a counter example to the claim.
5. All female employees make less than 55,000.
True.
How? Restrict domain to females (Betty, Ellen, Flo) and check claim.
6. All male employees make less than 55,000.
False
How? Restrict domain to males and check.
Al is a counter example
Note. To show that a universally quantified statement like
All P’s are Q’s.
Is true need to show every P has property Q.
To show false, just one single counter example (find a P that is not a Q)
Properties as sets.
5. All female employees makes less than 55,000.
Define E = the set of all employees. (our universe, domain)
= {Al, Betty, Carlos, Doug, Ellen, Flo}
F = the set of all female employees.
= {Betty, Ellen, Flo}
L = the set of employees making under 55,000
= {Betty, Carlos, Doug, Ellen, Flo}
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