Need help with 3.112, 3.113, 3.114, and 3.115

its, lowercase letters, uppercase letters, other)." In that example, we took "the password contains at least 3.4 and 3.15 construct a proposition corresponding to "the pa contains at least three of four character nd its analogues for the other character types) as an atomic proposition. But we could give a lower-level ion of valid passwords. Let isDigit, isLower, and isUpper be predicates that are true of single characters propriate type. Use standard arithmetic notation and these predicates to formalize the following conditions on a programming of the rdx(., ), where xi is the ith character in the password 3.112 is at least 8 characters long 3.113 x r contains at least one lowercase letter 4contains at least one non-alphanumeric character. (Remember that isDigit, isLouer, and tsupper 3.114 are the only predicates available!) 3.115 (Inspired by a letter to the editor in The New Yorker by Alexander George from 24 December 2007.) Steve s Martin, the great comedian, reports in Born Standing Up A Comic's Life that, inspired by Lewis Carroll he started closing his shows with the following line." (lt got big laughs In not oin home tonight: I'm going to Bananaland, a placehere oly tw thingste,oly too tings One all chairs are green and two, no chairs are green Born St Comic & Sch Steve Martin describes the joke as a contradiction-but, in fact, these two true things are not contradictory Describe how it is possible for both "all chairs in Bananaland are green" and "no chairs in Bananaland are green" to be simultaneously true