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Blast into Math! Pure mathematics: the proof of the pudding is in the eating

1. Statement: x =2. This statement means that x is equal to 2. The negation has the opposite
meaning: x is not equal to 2. So in this case the negation is

x =2.

2. Statement: 2+ x =4. The negation has the opposite meaning. So in this case the negation is

2+ x =4.

3. Statement: if A then B. This means: A implies B. If this statement is false that means A does

not imply B. So the negation of A implies B is: A does not imply B. Please be careful because
“A does not imply B” is different from “A implies not B.” A does not imply B means that:
there is at least one example in which A is true but B is not true. A implies not B means
that: every time A is true, B is not true. This is the same as: every time A is true, not B is
true. The negation of: “A implies B” can also be stated as: A does not necessarily imply B.

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