Difference between revisions of "Truth table proofs"
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{| class="wikitable" | {| class="wikitable" | ||
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! A !! B !! A ∧ B | ! A !! B !! A ∧ B | ||
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| true || true || true | | true || true || true | ||
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| + | A truth table can also be used to prove a logical identity. The following proves DeMorgan's law that ¬ (A ∧ B) is equivalent to (¬ A) ∨ (¬ B). Notice that the truth values for these (the last two columns in the table) are always the same. | ||
| + | |||
| + | {| class="wikitable" | ||
| + | |- | ||
| + | ! A !! B !! A ∧ B !! ¬ (A ∧ B) !! (¬ A) ∨ (¬ B) | ||
| + | |- | ||
| + | | false || false || false || true || true | ||
| + | |- | ||
| + | | false || true || false || true || true | ||
| + | |- | ||
| + | | true || false || false || true || true | ||
| + | |- | ||
| + | | true || true || true || false || false | ||
|} | |} | ||
Revision as of 14:49, 29 August 2022
Truth tables are used to show all possible values that a given logical expression might take. For example, the following gives the definition of the logical AND operation.
| A | B | A ∧ B |
|---|---|---|
| false | false | false |
| false | true | false |
| true | false | false |
| true | true | true |
A truth table can also be used to prove a logical identity. The following proves DeMorgan's law that ¬ (A ∧ B) is equivalent to (¬ A) ∨ (¬ B). Notice that the truth values for these (the last two columns in the table) are always the same.
| A | B | A ∧ B | ¬ (A ∧ B) | (¬ A) ∨ (¬ B) |
|---|---|---|---|---|
| false | false | false | true | true |
| false | true | false | true | true |
| true | false | false | true | true |
| true | true | true | false | false |
