Page 172 - Math Course 2 (Book 2)

Truth Tables and Logic

Key Concept Use the following statements to write a compound
statement for the conjunction ~p ^ r. Then find its
truth value.
Negation p: One foot is 14 inches.

q: September has 30 days.
Word If a statement is represented by p, then r: A plane is defined by three noncollinear points.
not p is the negation of the statement.
A foot is not 14 inches, and a
plane is defined by three
Symbols ~p, read not p Answer noncollinear points. ~p ^ r is true,
because ~p is true and r is true.

Conjunction
Truth Values of Disjunctions
A conjunction is a compound
Word statement formed by joining two or
more statements with the word and. Example

Symbols p ^ q, read p and q.
Use the following statements to write a compound
statement for the disjunction p or q. Then find its
truth value.
Disjunction p: AB is proper notation for “line AB.”

A disjunction is a compound q: Centimeters are metric units.
Word statement formed by joining two or r: 9 is a prime number.
more statements with the word or.
AB is proper notation for “line
v
Symbols p q, read p or q. AB,” or centimeters are metric
Answer units. p or q is true because q is
true. It does not matter that p is
false.

Let’s Begin Use the following statements to write a compound
statement for the disjunction q v r. Then find its
truth value.

Truth Values of Conjunctions AB is proper notation for “line AB.”
q: Centimeters are metric units.
Example r: 9 is a prime number.

Use the following statements to write a compound Centimeters are metric units, or
statement for the conjunction p and q. Then find Answer 9 is a prime number. q v r is true
its truth value. because q is true. It does not
matter that r is false.

p: One foot is 14 inches.
q: September has 30 days.
r: A plane is defined by three noncollinear points.

One foot is 14 inches, and
September has 30 days.
Answer
p and q is false, because
p is false and q is true.

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