Question

Write a Boolean expression that satisfies each of the following conditions:

1.The value of x is greater than 10 and y is less than or equal to 20.
2.Either a is equal to 5 or b is not equal to 10.
3.c is not greater than 15.
4.age is between 18 and 25 (inclusive).
5.The number n is even and greater than 10.

Answer 1

Here are Boolean expressions that satisfy each of the given conditions:

1. **Condition 1**: The value of \( x \) is greater than 10 and \( y \) is less than or equal to 20.
- Expression: \( (x > 10) \land (y \leq 20) \)

2. **Condition 2**: Either \( a \) is equal to 5 or \( b \) is not equal to 10.
- Expression: \( (a = 5) \lor (b \neq 10) \)

3. **Condition 3**: \( c \) is not greater than 15.
- Expression: \( (c \leq 15) \)

4. **Condition 4**: \( \text{age} \) is between 18 and 25 (inclusive).
- Expression: \( (18 \leq \text{age} \leq 25) \) or \( (\text{age} \geq 18) \land (\text{age} \leq 25) \)

5. **Condition 5**: The number \( n \) is even and greater than 10.
- Expression: \( (n \mod 2 = 0) \land (n > 10) \)

These expressions use standard Boolean operators: \( \land \) (and), \( \lor \) (or), and logical comparisons to establish the required conditions.