Is the following argument valid? If so, construct a formal proof (direct or indirect). If not,...

Is the following argument valid? If so, construct a formal proof (direct or indirect). If not, explain why not.

If Alex gets a new job, then he will buy a guitar.

If Alex wins the lottery, then he will buy a guitar.

If Alex goes to Costa Rica, then either Alex got a new job or Alex won the lottery.

Alex goes to Costa Rica.

Therefore, Alex bought a guitar.

Expert Solution

The given argument is correct.

Argument is that,

Alex goes to Costa Rica. Therefore, Alex bought a guitar.

Proof: Given that Alex goes to Costa Rica.

We know that if Alex goes to Costa Rica, then either Alex got a new job or Alex won the lottery.

Then we know that in either case, that is either he gets a new job or he wins a lottery then he will buy a guitar. Therefore we can conclude that if Alex goes to Costa Rica then he will surely bye a guitar.

Therefore the given argument is valid.

orchestra answered 2 years ago

Construct your own valid DEDUCTIVE arguments by applying the FIVE argument forms (rules) on the worksheet...

Construct your own valid DEDUCTIVE arguments by applying the FIVE argument forms (rules) on the worksheet below. You will need to insert your own example for each rule, following the form of the argument. A TRANSLATION KEY MUST BE PROVIDED FOR EACH EXERCISE (see above for an example). FORMS/RULES: Modus Ponens 1) If p, then q. 2) p. ------------------- 3) Thus, q. Modus Tollens 1) If p, then q. 2) Not q. ------------------- 3) Thus, not p. Hypothetical Syllogism 1)...

Suppose the economy is in a recession. Which of the following is a valid argument for...

Suppose the economy is in a recession. Which of the following is a valid argument for using expansionary fiscal policy, instead of monetary policy? Select one: a. Fiscal policy is more effective than monetary policy in a deep recession b. Fiscal policy is slower than monetary policy c. Fiscal policymakers are subject to more political influence, so some of their spending tends to be wasteful. d. Government spending could lead to lower growth through the crowding-out effect

Write a formal proof to prove the following conjecture to be true or false. If the...

Write a formal proof to prove the following conjecture to be true or false. If the statement is true, write a formal proof of it. If the statement is false, provide a counterexample and a slightly modified statement that is true and write a formal proof of your new statement. Conjecture: Let w, x, y, and z be single-digit numbers. The 4-digit number wxyz* is divisible by 9 if and only if 9 divides the sum w + x +...

Give a formal proof for the following tautology by using the IP rule. (A →B) ^...

Give a formal proof for the following tautology by using the IP rule. (A →B) ^ (B →C) →(A v B →C)

In the proof of Theorem 4.7 (Euclid’s proof that there are infinitely many primes), the argument...

In the proof of Theorem 4.7 (Euclid’s proof that there are infinitely many primes), the argument uses calculation of a number N. In each case below, suppose for the sake of demonstrating a contradiction, that the given list is the entire list of prime numbers. Calculate N and then factor N into primes to see that you do get a contradiction. (a) 2, 3, 5, 7, 11 (b) 2, 3, 5, 7, 11, 13, 17, 19 (c) 2, 3, 5,...

Explain the difference between a valid argument and a sound argument, and give an example of...

Explain the difference between a valid argument and a sound argument, and give an example of each.

Give a formal proof for the following tautology by using the CP rule. A v B→(¬...

Give a formal proof for the following tautology by using the CP rule. A v B→(¬ B →(A ^ ¬ B))

Determine if the following statements are true or false. In either case, provide a formal proof...

Determine if the following statements are true or false. In either case, provide a formal proof using the definitions of the big-O, big-Omega, and big-Theta notations. For instance, to formally prove that f (n) ∈ O(g(n)) or f (n) ∉ O(g(n)), we need to demonstrate the existence of a constant c and a sufficient large n0 such that f (n) ≤ c g(n) for all n ≥ n0, or showing that there are no such values. a) 10000n2 ∈ O(n4)....

Give a formal proof for the following tautology by using the CP rule. (A →(B →C))...

Give a formal proof for the following tautology by using the CP rule. (A →(B →C)) ^ B →(A →C)

Translate the following into standard form and symbolic form. Is it a valid or invalid argument?...

Translate the following into standard form and symbolic form. Is it a valid or invalid argument? Sound or unsound? Why? "Science and religion are basically the same. In religion, you believe something based purely upon faith. But in science, even if there is evidence, you have to have faith in your experiments and in the scientific method."" critical thinking a concise guide 4th edition, its not showing up on chegg study

Question