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© 2014 Pacific Crest
73
Symbol
Meaning
Name
Definition
A ↔ B
IS EQUIVALENT
TO, WHEN
logical
equivalence
A ↔ B is true if A and B have the same logical
content (the same truth values) for all possible
cases or models. A or B can usually be derived from
the other by the rules of logic (or mathematics).
Logical equivalence is often found in definitions.
Truth table
Examples of A ↔ B or A = B
A
B A
⇔
B
True True True
True False False
False True False
False False True
➊
A: John is eating strawberries
B. John is eating fruit from the genus
Fragaria
When
John is eating strawberries, John
is eating fruit from the genus
Fragaria
.
➋
A:
y
= 4
B:
y
+ 2 = 7
A
B A
↔
B
y
= 4
(True)
y
+ 2 = 7
(False)
False
Symbol
Meaning
Name
Definition
A ˄ B
AND
conjunction
A ˄ B is true when both propositions are true.
Truth table
Examples of A ˄ B
A
B A ˄ B
True True True
True False False
False True False
False False False
➊
A: A triangle has 3 sides
B: Picasso was an artist
A triangle has 3 sides
and
Picasso was an artist.
➋
A: 7 is prime
B: 12 is prime
A
B
A ˄ B
7 is prime
(True)
12 is prime
(False)
False
Symbol
Meaning
Name
Definition
A ˅ B
OR
disjunction
A ˅ B is true if either proposition is true. This is also
sometimes called an
inclusive disjunction
.
Truth table
Examples of A ˅ B
A
B A ˅ B
True True True
True False True
False True True
False False False
➊
A: Today is Friday
B: There’s only one Friday in each week
Today is Friday
or
there is only
one Friday in each week.
➋
A: 7 is prime
B: 12 is prime
A
B
A ˅ B
7 is prime
(True)
12 is prime
(False)
True
2.2 Logical Reasoning