Truth Tables — Mapping Every Case (Grades 7–8)
A truth table lists every combination of true/false inputs and the resulting output, so nothing is missed.
Understanding truth tables
For two inputs there are 4 rows. For "A AND B," the output is true only in the single row where both are true; for "A OR B," it's true in three rows (false only when both are false).
Seeing it in action
Worked example
For "A AND B," in how many of the 4 rows is the output true?
True only when A=true and B=true → 1 row.
| A | B | A AND B | A OR B |
|---|---|---|---|
| true | true | true | true |
| true | false | false | true |
| false | true | false | true |
| false | false | false | false |
Four rows cover every case. AND is true in 1 row; OR is true in 3.
A common mistake, and the fix
Missing a row, or reading OR as “one or the other, but not both”.
Two inputs give 4 rows: true-true, true-false, false-true and false-false. “A OR B” is true in 3 of them, including the row where both are true; it is false only when both are false.
Try a few
"A OR B": how many of 4 rows are true?
"A AND B" when A=true, B=false?
"A OR B" when A=false, B=false?
More logic & counting in Numeris.
Numeris doesn't have a star for truth tables yet, but its logic & counting constellation practises the skills around it.
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