Consider statements p and q. p: The truck is on the road. q: A valley is below us. (a) Write each statement below in symbolic form using p and q. Symbolic Descriptive form form OvO Statement 1: If the truck is on the road, then a valley is below us. Statement 2: If a valley is not below us, then the truck is not on the road. (b) Complete the truth table below. Use T for true and F for false. You may add more columns. But those added columns will not be graded. Your answers from part (a) will fill in here. Statement 1:|| Statement 2: T OvO T F O-0 F F F (c) Are Statement and Statement 2 equivalent? Why or why not? Choose the best answer. Statement 1 and Statement 2 are equivalent. This is because the truth value of O Statement 1 is the same as the truth value of Statement 2 for each true-false combination of p and q. Statement 1 and Statement 2 are equivalent. This is because the two statements are made from p and q, and any two statements made fromp and q are equivalent. Statement 1 and Statement 2 are not equivalent. This is because the two statements are different, and different statements cannot be equivalent. Statement 1 and Statement 2 are not equivalent. This is because the truth value of O Statement 1 is different from the truth value of Statement 2 for at least one true-false combination of p and q.

Consider statements p and q. p: More freshman chose to major in history than in nursing. q: Math was chosen by the fewest number of freshmen.

Translate the following statement into symbols. Then construct a truth table for the compound statement and indicate under what conditions the compound statement is true. You took out the trash or you did not leave the car a mess. p: You took out the trash. q: You left the car a mess. Use the truth table to determine the set of conditions that make the compound statement true. Choose the correct answer below. O A. The statement is true whenever p is false and q is true, and is false otherwise. OB. The statement is true whenever p and q are both true, and is false otherwise. OC. The statement is true whenever p is true or q is false, and is false otherwise. OD. The statement is true whenever p and q are both false, and is false otherwise. O E. The statement is true whenever p is true or q is true, and is false otherwise. PTT FE ott р Т Т

Learning Target Ol: I can use propositional variables and logical connectives to represent statements; and interpret symbolic logical statements in plain language. Let p, q and r be the propositions: p: It's over 100 degrees. q: It's too hot. r: I will bike today. 1. Interpret the expression (-p) Vr in plain language. 2. Interpret the expression p q in plain language. 3. Write the statement "If it is not too hot and it's not too over 100 degrees, then I'll bike today" in terms of the variables p, q, and r. 4. Write the statement "If I don't bike today, then it's too hot" in terms of the variables p, q, and r.