If A goes to the party, then B will not go. A) I only Explanation: From the first statement, we are given a condition and a result: "raining" as a condition and "I can't play soccer" as a result. Let us consider a revised version of the statements above and deduce whether the conclusion is true or false by Venn diagram. We make the wrong conclusion that rectangles also have this characteristic because it is known previously that both share a number of characteristics. & \text{(i)} & \text{Major in mathematics or computer science}\\ This does not make sense because it is not necessary for the condition to take place if the result occurs first. Inspector Aditya of the police extracts the following facts: (1)(1)(1) None other than Satvik, Krishna and Sharky was involved in the robbery. Isn't the proof by Venn diagram fun? If A goes to the party, then B will not go. "If and only if", sometimes written as iff and known as equivalence, is implication that works in both directions. "I used both baking powder and strawberry for my cake.". Note: To fix the conclusion, you should say "Some birds are chickens" instead of "All birds are chickens.". Propositional Logic Exercise 2.6. If Edward owns a bike, then … Welcome to logicproblems.org! Though they are the inverse and converse of the original statement, we must keep in mind that they might not necessarily be an error. Two and two makes 5. Propositional logic notation by problem solving. "\text{"If you are human, then you have DNA. Search for: Truth Tables and Analyzing Arguments: Examples. Log in. A propositional consists of propositional variables and connectives. For example, if we replace the word "wings" by "forearms" in the first statement, then the conclusion of "All chickens have forearms." This subsection explains why this proof (arguemnt) might not always work. ", (ii)\text{(ii)}(ii) Write down the two if-then statements for, "A polygon is a quadrilateral if and only if the polygon has 4 sides. Let's begin! Solve these word problems, with answers included. Log in. A full list of interactive Logic Proofs to solve. Thus we can say that all chickens have the same characteristics as a bird. Whenever an aspiring author writes on her blog, she writes every day for 3 straight consecutive days and then rests on the following day. This is known as an inverse error. Likewise, we can also verify or disprove statements. Stretch your analytic muscles with knights, knaves, logic gates, and more! Propositions Examples- The examples of propositions are-7 + 4 = 10; Apples are black. If Jeff does not finish his math homework, then he spent 5 hours playing video games. Because complex Boolean statements can get tricky to think about, we can create a truth table to keep track of what truth values for the simple statements make the complex statement true and false. Logic is the study of valid reasoning. Since you got a B\text{B}B average instead of a B+\text{B}^\text{+}B+ average, criteria (ii)\text{(ii)}(ii) is not satisfied. All chickens are birds. is purely an analogy and thus it is not an entirely accurate statement to begin with. Notice from the previous section that we've mentioned that "Q probably has property yyy too." "If it’s raining, then I can’t play soccer". I. Since you did not satisfy all the criteria and were turned down, the personnel didn't lie to you. \qquad Then, all yengs are yangs. Narendra Modi is president of India. Thus, we have started with a wrong premise. instead of "Q definitely has a property yyy too." During one particular week, she wrote on Thursday, Friday, and Saturday. Aria went to the school play. If Jeff finishes his math homework, then he did not spend 5 hours playing video games. It is given that Amy, Bernadette and Penny are good friends of Sheldon and Leonard. Let's see the following examples to see how the proof by analogy backfires: All squares and rectangless are convex, have four sides and form right angles at their vertices. But what's the benefit of this? Contrapositive: A statement is logically equivalent to its contrapositive. The elements of the propositional logic, like “ → ”, that we add to our language in order to form more complex sentences, are called “truth functional connectives”. implies that the set "all chickens" is a subset of "all birds." Explanation: From the first statement, we are given a condition and a result: "raining" as a condition and "I can't play soccer" as a result. If Edward owns a bike, then Freddy owns a bike. Taking the long view on your education, you go to the Prestige Corporation and ask what you should do in college to be hired when you graduate. Those who like paintings like flowers. Forgot password? Conclusion: If I can't play soccer, then it's raining. Johannes has several written publications on his bookshelf. Properties and Formulas of Conditional and Biconditional. Some pings are pongs. You might want to familiarize yourself with sets and Venn diagram first. What is the largest possible number that will go to the party? "}"If you are human, then you have DNA. I will try and simplify them as much as possible. It is pretty clear that the issue here is: there can be other reasons why I can't play soccer, which doesn't necessarily depend on the weather. Solving Logical equivalence & propositional logic problems without truth tables. However, there is no harm in checking whether they are correct or not. will inevitably be true despite its ridiculous claim. It seems that propositional logic word problems are interesting for pupils aged 9 to 16 years. You don't need to use actual words to formalize these statements. II. Therefore, all chickens have wings. If Jeff does well on his next math test, then he finished his math homework. Why does this work? What is the color of the dress Selena is wearing? \quad Some pings are pongs. & \text{(iii)} & \text{Take accounting}\\ If C goes to the party, then B will not go. Those who do not like music do not like flowers. "P if and only if Q" means that both "P implies Q" and "Q implies P". A typical propositional logic word problem is as follows: A, B, C, D are quarreling quadruplets. Sign up, Existing user? If these are all true, which of the following statements must be true? Take the statements below as an example, if the first statement is true, is the second statement also true? Like solving any other questions, we should always ask ourselves what we can and can't do when writing out our reasoning. \end{array}(i)(ii)(iii)Major in mathematics or computer scienceGet a B+ average or betterTake accounting. If C goes to the party, then B will not go. Let's try the following example. C) I and II only □_\square□. Therefore, all rectangles have sides of the same length. Let's do a brief recap for the application of Venn Diagrams by taking the following as an explicit example: Consider W,X,Y,ZW,X,Y,ZW,X,Y,Z as sets, each with their own elements in them. The converse statement implies that only if the weather is sunny then the day is Sunday, which is also ludicrous because they can also have a sunny weather on days not falling on a Sunday. The reason why proof by analogy works is because we make an inference that if the objects have multiple similar characteristics, and it is given that you know one of them have an extra characteristics (call it X), then it is not a bad inference to conclude that the other object shares that same characteristic X. "If I can’t play soccer, then it’s raining. }All humans are apes. 2. If Danny owns a bike, which of the following statements must be true? If Jeff spends 5 hours playing video games, then he cannot finish his math homework. Now that you're ready to solve logical problems by analogy, let's try to solve the following problem again, but this time by analogy! (i)\qquad \text{ (i)} (i) Write the inverse and converse of this statement. So the given conclusion is wrong because of the ridiculousness of the conclusion "Some humans are gorillas.". Explanation: By Venn diagram, the statement "A chicken is a bird" implies that the set "all chickens" is a subset of "all birds."