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Fundamentals of Logic
Statements/Propositions
– Sentences that are true or false but
not both. (Just like a simple boolean expression or conditional
expression in a programming language.)
For our purposes, statements will simply be denoted by
lowercase letters of the alphabet, typically p, q, and r. I will
refer to these as boolean variables as well.
Given simple statements, we can construct more complex
statements using logical connectives. Here are 4 logical
connectives we will use:
1)
Conjunction: This is denoted by the ‘
∧
’ symbol. The
statement p
∧
q is read as “p and q.” Only if both the values
of p and q are true does this expression evaluate to true.
Otherwise it is false.
2)
Disjunction: This is denoted by the ‘
∨
’ symbol. The p
∨
q is
read as “p or q.” As long as at least one of the values of p or
q is true, the entire expression is true
3)
Implication: This is denoted by the ‘
⇒
’ symbol. The
statement p
⇒
q is read as “p implies q”. Essentially, in a
programming language, this logic is captured in an if then
statement. If p is true, the q must be true. However, if p is
not true, there is no guarantee of the truth of q. An
important
observation
to
note:
when
statements
are
combined with an implication, there is no need for there to
be a causal relationship between the two for the implication
to be true.
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View Full DocumentConsider the following implications:
If my bread is green, then I will not eat it.
Here, if the bread is not green, that does not guarantee that I
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 Fall '09

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