Question

If the statement "If the sun is shining, then it's not raining" is assumed to be true, is its reverse, "If it's not raining, then the sun must be shining," also always true?

Answer 1

Answer:

No this is not always true.

Step-by-step explanation:

If the statement "If the sun is shining, then it's not raining" is assumed to be true, is its reverse, "If it's not raining, then the sun must be shining,"

No this is not always true.

Let s suppose,

A = The sun is shining  

B = It's not raining.  

The the statement "If the sun is shining, then it's not raining" translates in mathematical terms to :  

If A then B or A => B  

However if A => B is true then B => A may or may not be true as have too little information.  

So we cannot always say that "If it's not raining, then the sun must be shining,"

Answer 2

No, because it might be cloudy instead.

This is just like the statement, "All squares are rectangles" yet "All rectangles are squares" is not true.