Question

If a and b are odd integers, then a + b is an even integer.


Which is the inverse of the statement?

Answer 1

Given \(p\to q\), the inverse of this statement is \(\neg~p\to\neg~q\). The \(\neg\) symbol means "not".

Answer 2

.. please explain.. I'm in dumb mode right now..

Answer 3

Here's a sample statement: "If my name is John, then I am driving."

Here, let \(p\) represents my name being John and let \(q\) stand for "I am driving."

Symbolically, my statement becomes \(p\to q\).

The inverse of this statement is \(\neg ~p\to\neg ~q\).

So if \(p\) means my name is John, then \(\neg~p\) means my name is *not* John.

Similarly, \(neg~q\) means I am *not* driving.

So the inverse of \(p\to q\), or \(\neg~p\to\neg~q\), is, "If my name is not John, then I am not driving."

Does that make sense?

Answer 4

.... Um a bit.. so it would be if a and b are NOT integers then a+b are NOT even?

Answer 5

Yes, exactly.