Synergy User Manual and Tutorial. - THE CORE MEMORY
Synergy User Manual and Tutorial. - THE CORE MEMORY
Synergy User Manual and Tutorial. - THE CORE MEMORY
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<strong>Synergy</strong> <strong>User</strong> <strong>Manual</strong> <strong>and</strong> <strong>Tutorial</strong><br />
1 1 1 1<br />
This holds all combinations of F’s <strong>and</strong> T’s relative to the three simple statements.<br />
Remember the pattern in the columns <strong>and</strong> you wont have to count next time. Next mark<br />
the second set columns to be evaluated by precedence <strong>and</strong> fill in the truth-values.<br />
Because of the parentheses, the next columns will be the third <strong>and</strong> seventh.<br />
¬ (p ∨ q) ∧ (r ∨ p)<br />
T T T T T T<br />
T T T F T T<br />
T T F T T T<br />
T T F F T T<br />
F T T T T F<br />
F T T F F F<br />
F F F T T F<br />
F F F F F F<br />
1 2 1 1 2 1<br />
Negation has precedence over conjunction. Hence the first column is the negation of the<br />
third. To find the truth-values for conjunction, consider the highest values in the last row<br />
on each side, which is column one on the left <strong>and</strong> column seven on the right.<br />
¬ (p ∨ q) ∧ (r ∨ p)<br />
F T T T F T T T<br />
F T T T F F T T<br />
F T T F F T T T<br />
F T T F F F T T<br />
F F T T F T T F<br />
F F T T F F F F<br />
T F F F T T T F<br />
T F F F F F F F<br />
3 1 2 1 4 1 2 1<br />
The statement is only true for P(p, q, r) = P(F, F, T).<br />
Again if p, q <strong>and</strong> r were under consideration, values for p, q, <strong>and</strong> r will evaluate to true<br />
for Q(p, q, r) = (p→q)∧[(r↔p)∨(¬p)], construct a truth table for the statement. Also note<br />
that brackets [ ] <strong>and</strong> braces { } can be used to differentiate compound groupings up to<br />
three levels.<br />
(p → q) ∧ [(r ↔ p) ∨ (¬ p)]<br />
T T T T T T T T F T<br />
T T T F F F T F F T<br />
T F F F T T T T F T<br />
92
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