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In
logic, a conjunction is a compound
sentence formed by combining two sentences (or facts) using the
word "and."
A
conjunction is true only when BOTH sentences
(or facts) are true. |
Examples:
1.
"Blue is a
color
and
7 + 3 = 10."
(T
and
T =
T)
Since both facts are true, the entire sentence is true.
2. "One
hour = exactly 55 minutes and one minute =
exactly 60 seconds."
(F and
T = F) Since the first fact is false,
the entire sentence is false.
3. "3
+ 4 = 6 and all dogs meow."
(F and F
= F)
Since both facts are false, the entire sentence is false.
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Mathematicians
often use symbols and tables to represent concepts in logic.
The use of these variables, symbols and tables creates a shorthand
method for discussing logical sentences.
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Truth
table for conjunction (and):
(notice the
symbol used for "and" in the table below)
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A
truth table is a pictorial
representation of all of the possible outcomes of the truth
value of a compound sentence. Letters such as  and 
are used to represent the facts (or sentences) within the
compound sentence. |
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Remember:
For a conjunction (and)
to be true, BOTH facts
must
be true.
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