Synergy User Manual and Tutorial. - THE CORE MEMORY

Synergy User Manual and Tutorial
p∧q is true because “ice is cold” is true and “1 + 1 = 2” is true
p∧r is false because “ice is cold” is true and “1 + 1 = 11” is false
s∧q is false because “1 + 1 = 11” is false and “1 + 1 = 2” is true
r∧s is false because “water is dry” is false and “1 + 1 = 11” is false
All meaningful statements will have a truth-value. The truth-value of a statement
designates the statement as true T or false F. The statement p is either absolutely true or
absolutely false. If a compound statement’s truth-value can be determined in its entirety
based solely on its components, the compound statement is said to be truth-functional. If
a connective constructs compounds that are all truth-functional, the connective is said to
be truth-functional. Using these conditions it is possible to build truth-functional
compounds from other truth-functional compounds and connectives. As an example: if
the truth-values of p and of q are known, then we could deduce the truth-value of the
compound using the disjunction connective, p∨q. This establishes that the compound,
p∨q, is a truth-functional compound and disjunction is a truth-functional connective. A
truth table contains all possible truth-values for a given statement. The truth table for p
is:
because the simple statement p is either absolutely true or absolutely false. The
following is the truth table of p and q for the five previously mentioned operators:
p
T
F
p q ¬p ¬q p∨q p∧q p→q p↔q
T T F F T T T T
T F F T T F F F
F T T F T F T F
F F T T F F T T
Parentheses ( ) are used to group components into whole statements. The whole
compound statement p∧q can be negated by grouping it with parentheses and negating
the group ¬(p∧q). The table below shows all negated truth-values for the operators
previous table.
p q ¬(¬p) ¬(¬q) ¬(p∨q) ¬(p∧q) ¬(p→q) ¬(p↔q)
T T T T F F F F
T F T F F T T T
F T F T F T F T
F F F F T T F F
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