5) Describe the difference between disjoint sets and overlapping sets.

12) Suppose U = {a,b,c,d,e) and A = {a, b, c, e) and B = (c,d,e). Determine (An B).

1) Use the roster method to list the elements of the set consisting of: a) All positive multiples of 3 that are less than 20. b) Nothing (An empty set).

2) Let M = {all postive integers), N = {0,1,2,3... 100), 0= {100,200,300,400,500). Determine if the following statements are true or false and explain your reasoning. a) NCM b) 0 C M c) O and N have at least one element in common d) O≤ N e) o≤o 1

4) Which of the following universal sets has W = {12,79, 44, 18) as a subset? Choose one. a) T = {12,9,76,333, 44, 99, 1000, 2} b) V = {44,76, 12, 99, 18,900,79,2} c) Y = {76,90, 800, 44, 99, 55, 22} d) x = {79,66,71, 4, 18, 22,99,2}

3) What is the universal set that contains all possible integers from 1 to 8 inclusive? Choose one. a) A = {1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8} b) B={-1,0,1,2,3,4,5,6,7,8} c) C={1,2,3,4,5,6,7,8} d) D = {0,1,2,3,4,5,6,7,8}

A smallish urn contains 25 small plastic bunnies – 7 of which are pink and 18 of which are white. 10 bunnies are drawn from the urn at random with replacement, and X is the number of pink bunnies that are drawn. (a) P(X = 5) ≈ (b) P(X<6) ≈ The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles.  (a) The probability that the Grinch gets exactly 6 blue marbles is         [ Select ]      ["≈ 0.054", "≈ 0.043", "≈ 0.061"]  . (b) The probability that the Grinch gets at least 7 blue marbles is         [ Select ]      ["≈ 0.922", "≈ 0.905", "≈ 0.893"]  . (c) The probability that the Grinch gets between 8 and 12 blue marbles (inclusive) is         [ Select ]      ["≈ 0.801", "≈ 0.760", "≈ 0.786"]  . The Whoville small urn contains 100 marbles – 60 blue and 40 orange. The Grinch sneaks in one night and grabs a simple random sample (without replacement) of 15 marbles.  (a)…

Using Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates).

Consider the alphabet {a, b, c}.• Design a regular expression that recognizes all strings over {a, b, c} that have at least three nonconsec-utive c characters (two characters are non-consecutive if there is at least one character between them)and at least one a character.• Explain how your regular expression recognizes the string cbbcccac by clearly identifying which partsof the string match to the components of your regular expression