Logic / Unit 4 Logic 144 worked example, 60 to 90 seconds
Testing Equivalence and Consistency
The idea
Two statements are equivalent when their main columns match on every row, and a set of statements is consistent when at least one row makes every member true. Both verdicts are read directly off completed tables.
In practice
First, equivalence. Table the conditional p horseshoe q beside the disjunction of tilde p and q. Four rows each. The conditional reads true, false, true, true. The disjunction: tilde p is false, false, true, true, and joined to q by a wedge it reads true, false, true, true. Compare row by row — true and true, false and false, true and true, true and true. Every row agrees, so the two are equivalent. Now consistency. Take three statements: p horseshoe q, p, and tilde q. Build one table holding all three main columns. Scan for a single row where all three are true. Row one gives true, true, false. Row two gives false, true, true. Rows three and four both fail on p. No row makes all three true, so the set is inconsistent.
Where people slip
Equivalence needs agreement on every row, not on most of them. One differing row is enough to break it, and that row is often the last — which is why the comparison has to run to the end rather than stopping once a pattern looks established.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
Unlocks
- Nothing yet depends on this.
Something wrong in this lesson? Flag it · Sources for Logic