Question

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

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

Answer 1

To represent the specified conditions using Boolean expressions, we can combine them into a single expression as follows:

1. **The value of x is greater than 10**: \( x > 10 \)
2. **y is less than or equal to 20**: \( y \leq 20 \)
3. **Either a is equal to 5 or b is not equal to 10**: \( a = 5 \lor b \neq 10 \)
4. **c is not greater than 15**: \( c \leq 15 \)
5. **age is between 18 and 25 (inclusive)**: \( 18 \leq \text{age} \leq 25 \)
6. **The number n is even and greater than 10**: \( (n \mod 2 = 0) \land (n > 10) \)

Combining all of these conditions into a single Boolean expression, we have:

\[
(x > 10 \land y \leq 20) \land (a = 5 \lor b \neq 10) \land (c \leq 15) \land (18 \leq \text{age} \leq 25) \land ((n \mod 2 = 0) \land (n > 10))
\]

This expression combines the conditions using logical conjunction (AND, represented by \( \land \)) and disjunction (OR, represented by \( \lor \)).