Final answer:
To find the inputs that make the function f(x1, x2, ..., x17) = 0, we analyze each term in the function expression and determine the values that make the overall expression 0.
Step-by-step explanation:
A boolean function is a function that operates on boolean variables and returns a boolean value. In this case, the function f operates on 17 boolean variables, x1 to x17, and returns a value based on the expression (x2 + ¬x3 + ¬x7 + x11 + ¬x17), where ¬ represents the negation or complement of a variable.
To find the distinct inputs for which f(x1, x2, ..., x17) = 0, we need to find the values of x1, x2, ..., x17 that make the expression (x2 + ¬x3 + ¬x7 + x11 + ¬x17) equal to 0. Let's analyze each term in the expression:
- x2: This term can take either the value 0 or 1. If it takes the value 0, then the overall expression is 0 regardless of the values of the other terms. If it takes the value 1, then the overall expression is 1 unless the other terms are specifically chosen to make the expression 0.
- ¬x3: This term is the complement of x3, so it takes the value 1 if x3 is 0 and takes the value 0 if x3 is 1. To make the overall expression 0, x3 must be 1.
- ¬x7: This term is similar to ¬x3. To make the overall expression 0, x7 must be 1.
- x11: This term can take either the value 0 or 1. If it takes the value 0, then the overall expression is 0 regardless of the values of the other terms. If it takes the value 1, then the overall expression is 1 unless the other terms are specifically chosen to make the expression 0.
- ¬x17: This term is similar to ¬x3. To make the overall expression 0, x17 must be 1.
Based on the analysis above, the distinct inputs that make the function f(x1, x2, ..., x17) = 0 are:
x1 can take any value, x2 must be 1, x3 must be 0, x4 to x6 can take any values, x7 must be 1, x8 to x10 can take any values, x11 must be 1, x12 to x16 can take any values, and x17 must be 1.