Proposition & Converse

Transcript

Proposition & Converse Proposition and Converse A statement-and its reverse Swap the hypothesis and conclusion.A proposition is a statement which can be classified as true or false, but not both Example: 2 + 3 = 5 : This is true, so it is a proposition 7 is an odd number: This is false, so it is a proposition Mumbai is the capital of India: This is false, so it is a proposition These are not propositions What is your name? : It is a question Close the door : It is a command x + 2 = 100: Since we do not know the value of x, this can be true or false. So, it is not a proposition In this chapter, we will be dealing with If p, then q propositions We write it as p ⟹ q (or say p implies q) Example: If x = y and y = z, then x = z If a shape is a square, then it is a rectangle Converse If proposition is If p, then q Converse of proposition is If q, then p Example: Proposition: ”If you are a fish then you swim” The converse is "if you swim then you are a fish" The converse of a proposition is obtained by completely interchanging the hypothesis and conclusion. Proposition: ”If you are a fish then you swim” The converse is "if you swim then you are a fish" Another example Example: Squares and Rectangles Original: f a shape is a square, then it is a rectangle. Converse: FALSE If a shape is a rectangle, then it is a square. Rectangle, but not a square square has four right angles. A rectangle need not have four equal sides. A true statement can have a false converse.