Examples 3.4 and 3.15 construct a proposition corresponding to “the password contains at least three of four character types (digits, lowercase letters, uppercase letters, other).” In that example, we...

Examples 3.4 and 3.15 construct a proposition corresponding to “the password contains at least three of four character types (digits, lowercase letters, uppercase letters, other).” In that example, we took “the password contains at least one digit” (and its analogues for the other character types) as an atomic proposition. But we could give a lower-level characterization of valid passwords. Let isDigit, isLower, and isUpper be predicates that are true of single characters of the appropriate type. Use standard arithmetic notation and these predicates to formalize the following conditions on a password x = hx1, . . . , xni, where xi is the ith character in the password

1. x is at least 8 characters long.

2. x contains at least one lowercase letter.

3. x contains at least one non-alphanumeric character. (Remember that isDigit, isLower, and isUpperare the only predicates available!)