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.
Write out your final expression.

Answer 1

To create a Boolean expression that satisfies all of the given conditions, we can denote each condition as follows:

1. \( x > 10 \land y \leq 20 \)
2. \( a = 5 \lor b \neq 10 \)
3. \( c \leq 15 \)
4. \( age \geq 18 \land age \leq 25 \)
5. \( n \mod 2 = 0 \land n > 10 \)

Now, combining all these individual conditions into a single Boolean expression using logical conjunction (AND, denoted as \( \land \)) and disjunction (OR, denoted as \( \lor \)), we have:

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

This is the final Boolean expression that satisfies all the specified conditions.