# How to write a conditional statement

## Write the negation of the conditional statement. Is this fine?

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The negation of any statement $S$ is "It is false that $S$".

For your example, "If it is orange then it is not a banana", the negation is "it is false that if it is orange then it is not a banana".

Now, how could it be false that if it is orange then it is not a banana? I come to you in a bar. I say "I will bet you \$50 that whatever you come up with, if it is orange then it is not a banana." You say "I will take that bet." What can you do to win? Can you come up with some purple object and say "See, you are wrong!" Er, no. I was not talking about purple objects. I was talking about orange ones. I said that orange objects are not bananas.

Oh, now you understand. You reach into your pocket and take

out an orange banana. "Here is a thing that is orange and it is a banana! You owe me \$50!" "Drat!" I reply.

When you want to prove that it is false that if it is orange then it is not a banana, you cannot do it by coming up with purple grapes, or even with purple bananas. You have to come up with an orange banana.

The negation of your sentence "If it is orange then it is not a banana" is "It is orange and it is a banana".

Maybe it helps to take a less silly example. If I say "If a certain person is a politician, then they are not honest." You cannot disprove this by coming up up with an honest bus driver, or even a dishonest bus driver. The only way to falsify it is to come up with an honest politician. So the negation of this claim is "A certain person is a politician, and is honest."

Source: math.stackexchange.comCategory: Forex

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