Which rule of inference is used in the following argument, "If it snows today, then we will go skiing." "If it is snowing today; Therefore, we will go skiing" Modus tollens B) Unknown rule Modus Ponens Simplification
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- 4. Which rule of inference is used in the following argument? "Every student in this class studied for the exam. Ana is a student in this class. Therefore, Ana studied for the exam." a. Universal instantiation. b. Universal generalization. c. Existential instantiation. d. Existential generalization.6. For each of these arguments, explain which rules of inference are used for each step. a. "Doug, a student in this class, knows how to write programs in JAVA. Everyone who knows how to write program in JAVA can get a high paying job. Therefore, someone in this class can get a high-paying job" b. "Somebody in this class enjoys whale watching. Every person who enjoys whale watching cares about ocean pollution. Therefore, there is a person in this class who cares about ocean pollution"Indicate the most appropriate if-then statement that the English sentence represents: People 18 or older can vote in a Federal election. A. No if-then statement would cover this situation. B. If a person is 18 years old or older, then the person can vote in Federal elections. C. If a person does not vote in a Federal election, they are not 18 years old or older. D. If a pers is 18 years old or younger, then the person can vote in Federal elections.
- Question 25 The following two statements are logically equivalent: (p → q) ∧ (r → q) (p ∧ r) → q You can use truth tables to determine equivalency Group of answer choices True FalseIndicate the most appropriate if-then statement that the English sentence represents: People 18 or older can vote in a Federal election. If a person is 18 years old or younger, then the person can vote in Federal elections. No if-then statement would cover this situation. If a person is 18 years old or older, then the person can vote in Federal elections. If a person does not vote in a Federal election, they are not 18 years old or older.“The fish is fresh or I will not order it. The fish is fresh. Therefore, I will order it.” 2. “If she doesn’t get on the plane, she will regret it. She does not regret it. Therefore, she got on the plane.” The validity of an argument can be determined using a truth table. We proceed as follows: Write the argument in symbolic form. Construct a truth table that shows the truth value of each premise and the truth value of the conclusion for all combinations of truth values of the simple statements. If the conclusion is true in every row of the truth table in which all the premises are true, the argument is valid. If the conclusion is false in any row in which all of the premises are true, the argument is invalid.
- With these hypothesis: “It is not sunny this afternoon and it is colder than yesterday” “We will go swimming only if it is sunny” “If we do not go swimming, then we will go hiking” “If we go hiking, we will see rattle snakes” Using the rules of inference, construct a valid argument for the conclusion: “we will see a rattle snakes”answer only know else strict action dont answer else compliantFour mathematicians have a conversation, as follows: ALICE: I am insane. BOB: I am pure. CHARLES: I am applied. DOROTHY: I am sane. ALICE: Charles is pure. BOB: Dorothy is insane. CHARLES: Bob is applied. DOROTHY: Charles is sane. You are also given the following information: Pure mathematicians tell the truth about their beliefs. Applied mathematicians lie about their beliefs. Sane mathematicians' beliefs are correct. Insane mathematicians' beliefs are incorrect. With the preceding clues, classify the four mathematicians as applied or pure, and insane or sane. Briefly explain your logic.
- Refer to the following statement to answer parts (a) through (c) below, The professor is intelligent and an overachiever, or not an overachiever a. Write the statement in symbolic form Assign letters to simple statements that are not negated Choose the correct answer below OA. let p=The professor is intelligent and letq= The professor is not an overachiever, (p A q)v OB. let p= The professor is intelligent and let q= The professor is not an overachiever (p v q) A OC. let p= The professor is intelligent and let q= The professor is an overachiever (p A q) v -q O D. letp=The professor is intelligent and let q= The professor is an overachiever, (p v q) ^ -9 b. Construct a truth table for the symbolic statement in part (a) PAq (pAq) v -q T.A proposition s is given. s: "2+9=15" The negation of the proposition s is "2+9=11" YES cannot be decided NO OTHERThe set of premises and a conclusion are given. Use the valid argument forms to deduce the conclusion from the premises, giving a reason for each step. Assume all variables are statement variables. a. p>9 b. rVs c. ~s >-t d. ~q Vs C. e. ~S f. ~pAr>u g. w Vt h. uAw