(Logic and Truth Tables MC)Complete the truth table for the given logical statement: p ∨ ∼q

(Logic Operations and Equivalence MC)Use the statements and truth table to determine which statements are equivalent.p: It is a fish.q: It eats algae. p q ∼p ∼q p → q ∼p → ∼q q → p ∼q → ∼p T T F F T T T T T F F T F T T F F T T F T F F T F F T T T T T T

(Applying Two-Way Frequency Tables LC)P(A) = 0.27, P(B) = 0.40, and P(A∩B) = 0.108. Are events A and B independent? Justify the answer mathematically.

(Interpreting Independence LC)P(A) = 0.53 and P(B) = 0.14. Determine P(B|A) if events A and B are independent.

(Events and Sample Spaces HC)A Venn Diagram shows Sets A and B.Part A: Determine the elements in A ∩ B. Justify the answer using the Venn Diagram. (2 points)Part B: Determine the elements in ~(A ∩ B). Justify the answer using the Venn Diagram. (3 points)Part C: Determine the elements in A ∪ B. Justify the answer using the Venn Diagram. (2 points)Part D: Determine the elements in A ∪ ~B. Justify the answer using the Venn Diagram. (3 points)

(Set Operations and Relations LC)Given A = {1, 3, 6, 9} and B = {3, 4, 7}, determine A x B.

(Interpreting Independence HC)The table summarizes the daily caffeine habits and majors of students at one university. Coffee Energy Drink No Caffeine STEM Major 0.32 0.13 0.02 Not STEM Major 0.17 0.27 0.09 Part A: Determine P(no caffeine | STEM major) and describe the event in everyday language. Show all work. (5 points)Part B: Are the events consuming no caffeine and a STEM major approximately independent? Use probabilities to justify the answer. (5 points)

(Interpreting Independence MC)There is a 25% chance that a book has a red cover, a 32% chance that a book is fiction, and a 16% chance that a book is fiction with a red cover. Determine whether the events “red cover” and “fiction” are approximately independent events. Justify mathematically.

(Addition and Multiplication Rules for Probability MC)A cafe offers 9 types of coffee, 5 types of tea, and 4 types of soft drinks. Determine the total number of beverages from which a customer can choose.

(Set Operations and Relations MC)Given U = {g, h, i, j, k, l, m, n, o, p}, A = {g, h, m, o, p}, and B = {h, j, k, m, n, p}. If A′ ∩ B′ = {i, l}, determine (A ∪ B)′.