## Truth Tables and De Morgan's Rules

Read this chapter, which discusses Boolean variables as used in decision tables. Truth tables are used to collect variables and their values relative to decisions that have to be made within control structures.

### 2. Review of Truth Tables

**Answer:**

Assume that `x`

contains 9 and `y`

contains 7.

The expression evaluates to **False**. One way to show this is below.

# Review of Truth Tables

A **truth table** shows the evaluation of a boolean expression.

- Each row of a truth table starts with a selection of truth values for the operands.
- There is one row for each possible selection of truth values.
- The columns show the truth value of expressions and subexpressions containing the operands.

The table at right has four rows for the truth values, one row for each of the four possible choices for the two operands. (The operands are the relational expressions `x<12`

and `y>10`

.) The last column shows the result of the `&&`

operator with those values.

Operands | Boolean Expression | |
---|---|---|

x < 12 | y > 10 | x < 12 && y > 10 |

F | F | F |

F | T | F |

T | F | F |

T | T | T |

**Question 2:**

What row of the table is used when `x`

contains 1 and `y`

contains 23?