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In this presentation we will take a look at conditional statements of the form p ! q and introduce the converse, the inverse and the contrapositive of such conditional statements. the converse of this statement is q ! p, the inverse of this statement is :p ! :q, the contrapositive of this statement is :q ! :p. If it rains, then 2 + 2 = 4.
1 What is a Contrapositive? A Counter-Example? A Converse? Our goal is to get to the point where we can do the contrapositive mentally. In other words, we want to be able to read a conditional statement (if P then Q) and immediately \see" the contrapositive. There are many reasons that this is useful.
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In Korean: 이 더하기 이는 사 (i deo-ha-gi i-neun sa) Let’s break it down. 이 (2) 더하기 (plus) 이 (2) 는 (equals) 사 (4) Also note that for equals, you would use 는 if the last syllable is a vowel and 은 if the last syllable is a consonant. How about subtraction? 5-3 = 2. 오 빼기 삼은 이 (o bbae-gi sam-eun i) 오 (5) 빼기 (minus) 삼 (3) 은 (equals) 이 (2) Now multiplication:
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How does the converse of a conditional statement differ from the original statement, and why is this distinction important in mathematical proofs? The converse of a conditional statement switches the hypothesis and conclusion, making it essential to evaluate its truth separately from the original.
