EXERCISE 1.13.1: Proving the validity of arguments with quantified statements. Prove that the given argument is valid. First find the form of the argument by defining predicates and expressing the hypotheses and the conclusion using the predicates. Then use the rules of inference to prove that the form is valid. (a) The domain is the set of musicians in an orchestra. Everyone practices hard or plays badly (or both). Someone does not practice hard. : Someone plays badly. (b) The domain is the set of people who live in a city. Linda lives in the city. Linda lives in the city. Linda owns a Ferrari. Everyone who owns a Ferrari has gotten a speeding ticket. : Linda has gotten a speeding ticket. (c) The domain is the set of all paintings. All of the paintings by Matisse are beautiful. The museum has a painting by Matisse. : The museum has a beautiful painting.

Proofs: Construct proofs to show that the following symbolic arguments are valid.  Commas mark the breaks between premises, ‘∴’ precedes the conclusion. You may use any rule, but you must use CP (H∨E)→K ∴E→K

If I study hard, I will graduate with flying colors. If I graduate with flying colors, I will be employed in a good company. If I will be employed in a good company, I will get rich. | am poor. I will study hard, or I will get married. Therefore, I will get married. In proving this argument, what rule of inference is used below: If I study hard, I will be employed in a good company. If I will be employed in a good company, I will get rich. Therefore, If I study hard, I will get rich. A Modus Tollens В Addition C) Hypothetical Syllogism D Disjunctive Syllogism

Exercise 1.1.3: Applying logical operations. infoAbout Assume the propositions p, q, r, and s have the following truth values: p is false q is true r is false s is true What are the truth values for the following compound propositions? (a)    ¬p (b)    p ∨ r (c)    q ∧ s (d)    q ∨ s (e)    q ⊕ s (f)    q ⊕ r

Discrete Math! Look at image. Thanks

EXERCISE 1.11.1: Valid and invalid arguments expressed in logical notation. Indicate whether the argument is valid or invalid. For valid arguments, prove that the argument is valid using a truth table. For invalid arguments, give truth values for the variables showing that the argument is not valid. (h) (1) q→p -q Ap -(p→q) 9 p -q -(p→q) Р q→P q→P P :-(p→q)

Use the rules of inference and the laws of propositional logic to prove that each argument is valid. Number each line of your argument and label each line of your proof "Hypothesis" or with the name of the rule of inference used at that line. If a rule of inference is used, then include the numbers of the previous lines to which the rule is applied. 비 (c) (d) D EXERCISE 1.12.2: Proving arguments are valid using rules of inference. → P→ (q^r) -q -P (p^q) →r -r 9 :-P (pvq) →r p Ar pvq -pvr -q p→q r-u par q^u Feedback?