## Proof Necessary and Sufficient Conditions

Why should one person ever accept as true a statement made by someone else? The usual response would be, "Prove it!" If the statement is a purely factual one, for example, "prices have risen." then proof would lake die form of some factual evidence that substantiates the statement. Economics is more often concerned, however, with deductive statements such as:

// the money supply increases, then the price level will rise.

which is to say. increases in the money supply lead to inflation. A stronger statement is:

The price level rises if and only if the money supply increases.

which is to say. only increases in the money supply lead to inflation. We are interested in how statements of this type are proved.

It is useful to express such statements in a general symbolic notation We introduce the symbol for the relation "if then," and the symbol "o" for "if and only if." We use capital letters such as p and q to stand for basic statements such as "the money supply increases" (P) or • prices rise" (Q). We could then write the statements above as

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