Suppose we have a specially -adapted typewriter for Monkeys to use that has only keys: A B C DE KL M N O P W X Y Z Important All of your solutions must be clearly justified with explanations and you must writ each of your final answer in two ways. - As a formula involving only products, sums, differences, or powers. - As one final concrete number (where you might need to make use of a calculator) Using the monkey typewriter, how many 13-letter words are there consisting of 13 distinct lette that begin with ABC' or end with 'MÕNKEY'? (this is an inclusive or ) ( letters may not be repeated

The domain of discourse for this problem is a group of three people who are working on a project. To make notation easier, the people are numbered 1, 2, 3. The predicate M(x, y) indicates whether x has sent an email to y, so M(2, 3) is read "Person 2 has sent an email to person 3." The table below shows the value of the predicate M(x, y) for each (x, y) pair. The truth value in row r and column y gives the truth value for M(x, y). M | 1 2 | 3 1 TTT 2 TFT 3 TT|F Determine if the quantified statement is true or false. Justify your an- swer. (a) Væ Vy (x # y) → M(x, y)) (b) Væ3y ¬M(x, y) (c) 3r Vy M(x, y)

Matt has six times as many stickers as David. If David has d stickers and Matt has m stickers, and Matt gives David 5 stickers, how many stickers does each have in terms of d? In terms of d, how many stickers does Matt have, after giving David 5 stickers? (Type an expression using d as the variable.) In terms of d, how many stickers does David have, after getting 5 stickers from Matt? (Type an expression using d as the variable.)