Converse of a conditional statement

Question

In the conditional statement If 5+5=20, then 3+2=5 how can the conditional be true when one part of the statement is not true ie 5+5=20 is not true.

then the converse of that says If 3+2=5, then 5+5=20 but it says it is false??

I am homeschooling my kids and have been doing great (out of school for almost 30 years now) but this has me stumped?

thanks

Misti

Answer 1

Take a look at youtu.be/ptIiMib9c9E

Answer 2

Conditional statements are composed of two parts: the part following the "if" is called the premise, the part following the "then" is called the conclusion.

A conditional statement is defined to be true whenever the premise doesn't hold. Thus, the statement If 5 + 5 = 20, then 3 + 2 = 5 is by definition true, since the premise isn't true. On the other hand, the converse, If 3 + 2 = 5, then 5 + 5 = 20, is false, because the premise holds but the conclusion does not. That is the only circumstance under which we say a conditional is false: the premise holds but the conclusion doesn't.

The given conditional statement is likely trickier because conditionals are sort of meant to include a premise that may or may not hold, which is not so in the given statement.

Consider a more realistic / useful conditional in the context of geometry: If quadrilateral ABCD is a square, then it is a rectangle.

This is a true statement, since all squares are rectangles. And if we have a quadrilateral ABCD that is not a square, then we don't know if the conclusion holds or not. I.e. ABCD may or may not be a rectangle, and the conditional statement is both true and irrelevant.

Btw, the converse of this statement is false: If quadrilateral ABCD is a rectangle, then it is a square. In geometry, it is important to distinguish between a conditional and a biconditional statement, the latter of which is true and its converse is also true: If a quadrilateral is a parallelogram, then it has a pair of opposite sides that are parallel and congruent.