- #1

Rishabh Narula

- 61

- 5

- TL;DR Summary
- I was looking up the meaning of vacuously true statement and why false implies truth.

Have I understood it correctly?

We say that an implication p --> q is vaccuously true if p is false.

Since now it's impossible to have p true and q false.

That is we can't check anymore whether the contrary, p being true and q being false,can be.Since p being true is non-existent.

So we take the implication as true.

For eg. If 3 squared = 27,then 2+2=5.

Can we check if it is indeed true that 3 squared equals 27 then 2+2 is not 5.

No.

Because 3 squared equals 27 is non-existent. Or false.

So we can't check if the statement is false.

Hence it must be true.

Since now it's impossible to have p true and q false.

That is we can't check anymore whether the contrary, p being true and q being false,can be.Since p being true is non-existent.

So we take the implication as true.

For eg. If 3 squared = 27,then 2+2=5.

Can we check if it is indeed true that 3 squared equals 27 then 2+2 is not 5.

No.

Because 3 squared equals 27 is non-existent. Or false.

So we can't check if the statement is false.

Hence it must be true.