It's clear what actions existing customers are taking on your website and mobile app. You want to take your social optimization efforts to the next level and estimate the future behaviors of your customers based on historical data. What type of analytics should you reference when looking ahead with social media measurement? predictive analytics descriptive analytics prescriptive analytics

2) a) Determine the whether the following expression is tautology, contradiction or contingency. i) \( \quad p \rightarrow((q \vee r) \wedge(p \wedge q)) \). ii) \( \quad p \vee q \leftrightarrow(r \wedge q) \).

Part B Eating daily from all the food groups will give you a balanced diet. Name the basic food groups.

12. Given set \( \mathrm{A}=\{\emptyset,\{\emptyset\}, 0\} \), which of the following is true? C. \( \emptyset \subseteq A \) B. \( \{\emptyset\} \in A \) C. \( \{\{\emptyset\}\} \subseteq A \) D. All are correct 13. For any sets \( A \) and \( B \) which of the following is true. A. If \( B \subseteq A \), then \( B^{\prime} \subseteq A^{\prime} \) C. \( A-B=A \cap B^{\prime} \) B. If \( A \subseteq B \), then \( A \cup B=B \) D. all except A. Part Three: solve the following problems. 1. For any propositions \( p \) and \( q \), determine whether \( (p \wedge q) \Rightarrow(q \wedge \neg p) \) is tautology, contradiction or neither? 2. Show that the argument: \( p \Rightarrow q, \neg p \Rightarrow h, h \Rightarrow k \vdash \neg q \Rightarrow k \) is valid. 3. Let \( \mathrm{U}= \) the set of one digit counting numbers \( A=\{x: x \) is an even number in \( U\} \) \( B=\{x: x \) is a square number in \( U\} \) \( \mathrm{C}=\{x: x+2<10 \), where \( x \in U\} \), then find the following. A. \( (A \cup B) / C \) C. \( \left(A \cap B^{\prime}\right) \Delta C \) B. \( (A \Delta B) / C \) D. \( \left(A \cap B^{\prime}\right)^{\prime} \) 4. Write the converse, inverse and contrapositive of the conditional statement. "If it is cold or rainy, I will not take a walk."

¿Qué es un cuantificador en lógica matemática? a) Un número que representa una cantidad fija b) Un simbolo que indica cuántos elementos de un conjunto cumplen una propiedad c) Un tipo de operacion matemática d) Una variable algebraica

Part II. The following problems have exactly one best answer. Chose the correct answer. 1. Which of the following compound propositions is necessarily true? A. \( p \wedge \neg p \) C. \( p \Leftrightarrow \neg p \) B. \( p \vee \neg p \) D. . \( (p \vee \neg p) \Rightarrow p \) 2. Which of the following represents a set? A. The Collection of good students in a class. C. \( \{a, b\}, c \). B. The collection of cows with 6 legs. D. The collection of interesting birds. 3. Which of the following is a proposition? A. What is your name? C. May God bless you! B. \( 2 x-3=0 \) D. 123 is a prime number. 4. Let A be any set and \( \mathrm{P}(\mathrm{A}) \) be the power set of A , which of the following is true? A. \( \{\varnothing\} \subseteq A \) B. \( \emptyset \in A \) C. \( \emptyset \in P(A) \) D. \( A \subseteq P(A) \) 5. Which of the following statement is true? A. \( (\forall x \in R)(\exists y \in R)(2 x+y=-4) \) C. \( (\forall x \in R)(\exists y \in R)(x y=1) \) B. \( (\exists x \in R)(\exists y \in R)(|x y|=-3) \) D. \( (\exists x \in R)(\forall y \in R)(2 x+y=-4 \) 6. Let A be any set with certain number of elements, then which of the following is false? A. A may contain 5 proper subsets C. A may contain 16 subsets B. A may contain only one proper subset D. A may contain only one subset 7. Let p and q be propositions which of the following implies that. \( p \wedge q \) is true. A. . \( p \vee q \) is true B. . \( \neg p \wedge q \) is false C. \( p \Rightarrow q \) is true D. \( p \Rightarrow \neg q \) is false