![]() ![]() There are some other special ways of modifying implications. We want to switch the hypothesis and the conclusion, which will give us: "If something has seeds, then it is a watermelon." Of course, this converse is obviously false, since apples, cucumbers, and sunflowers all have seeds and are not watermelons. Write the converse of the statement, "If something is a watermelon, then it has seeds." To highlight this distinction, mathematicians have given a special name to the statement q → p: it's called the converse of p → q. It's kind of like subtraction: 5 – 3 gives a different answer than 3 – 5. In other words, p → q and q → p mean very different things. The hypothesis and conclusion play very different roles in conditional statements. In (B), we may rewrite the statement as "If I peel rutabagas, then I cut off a finger," telling us that p = "I peel rutabagas" and q = "I cut off a finger."įinally, we may rewrite (C) as "If it is a dog, then it will go to heaven," yielding p = "it is a dog" and q = "it will go to heaven." (B) I cut off a finger whenever I peel rutabagas.įor (A), p = "it rains outside" and q = "flowers will grow tomorrow." (A) If it rains outside, then flowers will grow tomorrow. ![]() Identify p and q in the following statements, translating them into p → q form. In fact, the old saying, "Mind your p's and q's," has its origins in this sort of mathematical logic. However, mathematicians can be drier than the Sahara desert: they tend to write conditional statements as a formula p → q, where p is the hypothesis and q the conclusion. ![]() Some ways to mix it up are: "All things satisfying hypothesis are conclusion" and " Conclusion whenever hypothesis." The same is true of conditional statements: after a while, the If-Then formula becomes a real snoozefest. As your English teacher would say, good writers vary their sentence structure. ![]()
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