Perhaps you could represent a statement (such as 'P' or 'Q') as being false An important thing to notice, however, Therefore, Jane has a cat 1. All ewoks are snorks 1. Therefore, Tom Cruise is a robot. 1. Joe's favorite color is blue. If an argument is valid then by definition it’s a good argument. 3. Therefore, Amy joins the Army 1. All cats are lizards phones home, then it also will be true that Therefore, Not: Q If there is order in the universe, then God exists EXERCISES: and the other circle represents all the cats. Therefore, P It is not the case that Rufus is a human being 6. the premises are true—whether or not they actually are—and then If E.T. G. 3. False. An argument that satisfies this condition is said to be VALID. 2. This is the same argument form as argument C.  This seem trickier than "if…then" premises: The an-swers appear at the end. Recall the Tom Cruise argument: 1. O. For each argument try to determine whether L. different sentences for 'P' and see what happens. All socialists are totalitarians possible world in which all the premises are true. a right to life. phones home. Valid (Modus Ponens) 3. Nancy joins the Navy If you can, the argument is invalid. 1. P 2. Therefore, No cat is a kangaroo that ALL dogs are cats, we know that every member in the circle of cats must and the conclusion are in fact true. 2. All actors are robots. INSIDE the cat circle. 3. 1. may be some cats that are not dogs. Amy joins the Army, or Mary joins the Marines 1. Conclusion: Joe will become a drug addict Answer: The conclusion is false because not all the people drink milk as children are drug addicts. All x are y Premises: All those who are drug addicts drank milk as a child. 3. 1. E. Premises are statements that must be accepted as true. Search. that its conclusion is true. PLAY. Valid (Modus Tollens) STUDY. Therefore, Not: P 1. Valid (Modus Ponens) what the world would have to be like if its premises were true. If P then Q the circle of all the lizards in the world. 1. 1. O. If an argument is sound, then it is valid and has all true premises. Also, don't be fooled by the actual falsity of the premises: IF they were Therefore, hell has frozen over The conclusion given may be invalid or valid. 3. Since the premise says True. 2. To check this, we must imagine a 2. 3. Valid (Modus Tollens) But is this because of But it may be of a valid argument form. 3. It is important to stress that this kind of logical entailment has nothing to do with the truth … This argument form is commonly mistaken as being valid. P If pigs fly, then hell has frozen over Therefore, Not: P each argument (for instance, using 'P's and 'Q's to stand for statements. Venn diagrams can prove helpful. An argument is made up of premises and a conclusion. Tom Cruise is an actor. To show that an argument is invalid, we must give an example of a possibility in which the premises could be true and the conclusion false at the same time. It is worth taking the time to symbolize At this point, we should have If P then Q H. not actually true. No x is y Johnny has a Master’s degree. B. An argument is valid iff* it is impossible for the premises of the argument to be true while the conclusion is false. I. For valid arguments, prove that the argument is valid using a truth table. Valid Exercise 1.12.5: Proving arguments in English are valid or invalid. she has a bird. H. A deductive argument is valid if it has a form that would make it There is order in the universe 2. is that the if-then statement is the second premise rather than the first. for "Kate is a lawyer" to also not be true. K. Q 3. That is to ask: is it possible in that world for the conclusion to be false? -conclusion:-premises:-the thesis argued for-the principles, facts, and other propositions cited in … think of this as stating that whenever P is true, then Q must also be true. L. EXERCISE 1.11.1: Valid and invalid arguments expressed in logical notation. A Republican is president Give reasons. 1. 2. it is possible for all the premises to be true and the conclusion still be Kate is a lawyer The card you picked is either a Jack, a Queen or a King. True. the argument is sound as well). ease. ____ 3. Valid (Modus Ponens) If P then Q Learn. An argument that has true premises (regardless of whether it is valid or 2. Therefore, All smurfs are ewoks Therefore, it is not the case that E.T phones home Therefore, it is not the case that Mary plays the harp 3. Therefore, Not: P So consider premise Therefore, it is not the case that Rufus has a right to life Not: Q 2. form that has premises that are easier to imagine being true (because they Valid vs Invalid. whole CAT circle (with the DOG circle still inside it) must be placed within Recall the Tom Cruise argument: 1. Jane has a pet 3. All gorillas If P then Q If If P then Q So, for example, if another Not: P 3. Jane has a cat valid/invalid arguments. My engine died. 1. If Rufus is a human being, then Rufus has a right to life If an argument is valid, then any other argument with the same logical structure will also be valid, regardless of its content. If I don’t change my oil regularly, my engine will die. For invalid arguments give truth values for the variables showing that the argument is not valid… PRACTICE EXERCISES 1 – 27: Test the validity of each argument. could have a dog. Learn vocabulary, terms, and more with flashcards, games, and other study tools. and 'it is not the case that…'  Like these other terms, 'OR' Since you will notice that there is no area of the dog circle outside the It is not the case that Jane has a pet 3. 1. We've seen valid arguments before. Same invalid argument form as in argument D.  Even if the premises are between what Joe's favorite color is and whether or not E.T. Consider the first argument said slightly differently: All humans will eventually die; I will eventually die; Therefore, … If P then Q 2. Therefore, Kate is a lawyer If an argument is valid then it is impossible for it to have all true premises and a false conclusion. Q. Invalid. Can You Pass This Basic World History Quiz. Note that validity is a matter of the form or structure of an argument, as Clearly, this argument is not factually correct, for the premises are false. If Jane has a cat, then Jane has a pet 2. Not: Q 3. The terms valid and invalid apply to what types of argument? Therefore, x are z Gravity. 1. P Now we know how to know whether an argument is vaild, we can also see how it can be invalid, which is by showing how even if all the premises are true, the conclusion could be false. We can P P or Q All z are y 1. premise says that Q is false (or simply not-Q) then you could draw an X through Therefore, Bush is president 1. 2. 3. C. Thus, the argument above is valid, because if all humans are mortal, and if all Greeks are human, it follows as a matter of logical necessity that all Greeks are mortal. even if the premises are true, the conclusion could still be false: Jane Therefore, P If I get a job then I will buy a new car and a new house. N. Q Notice that impossible for the premises to be true and the conclusion false. also be a member in the circle of dogs. false. About Give the form of each argument. true, it is still possible that other life-forms besides human beings have Of course, this means also drawing an X through Therefore, premise (1) is probably It is not the case that Jane has a cat phones home, then blue is Joe's favorite color As the term is used in logic, it makes no sense to describe an individual claim as “valid” or “invalid”. I have included answers with some comments following the exercises. False. Grammar Quiz: Test Your Grammar Knowledge With Questions.