Math: The Statement and the Contrapositive

For a few years, this topic fell from view.  As a math tutor, I’m glad to see it back.

To a person studying logic, the statement “p implies q” also means “if p, then q”.  It can also be written


Example of a statement:

If a minute has passed, then sixty seconds have passed.

p and q, by themselves, might be called assertions.  Therefore, in the above statement, “a minute has passed” is an assertion.  So is “sixty seconds have passed.”

To form the contrapositive of a statement, you reverse its order, then negate both parts of the statement:

If sixty seconds have not passed, then a minute has not passed.

In logic notation, you negate an assertion by writing a line above it:

It follows that the construction of the contrapositive is

I’m told that, in general terms, the contrapositive is the logical equivalent to the statement itself. From what I’ve seen myself, I’ve no cause to doubt that assertion:)

There are other logical derivatives of a statement: the converse and the inverse, to name a couple. I’ll discuss them in future posts:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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