Logic Worksheet With Answers Page 2
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22b. The negation of the statement “Today is not raining” is “Today is raining” or “It is not
true that today is not raining”.
Symbolically, the negation of a statement p is denoted by ~p.
Ex:
p:
Today is Sunday;
~p:
Today is not Sunday.
The words all, some, and no (or none) are called quantifiers.
Ex: Statements containing a quantifier:
All poets are writers.
Some people are bigots.
No math books have pictures.
Some students do not work hard.
Equivalent Ways of Expressing Quantified Statements
Statement
Equivalent way to express it
Example
All A are B
There are no A that are no B
All teachers are trained;
There are no teachers that are
not trained.
Some A are B
There is at least one A that is
Some people like ice-cream;
in B
At least one person likes ice-
cream.
No A are B
All A are not B
No car is running on the rail
train;
All the cars are not running on
the rail train.
Some A are not B
Not all A are B
Some students do not pass the
class;
Not all of the students are
passing the class.
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