# If false imples true then you can’t make statements about real life? Confused

## Why does false imply true true?

So the reason for the convention ‘false implies true is true’ is that it makes statements like x<10→x<100 true for all values of x, as one would expect.

## Do two Falses make a true?

No. Formal logic (valid reasoning) guarantees only that from true statements, a false conclusion (statement) cannot be deduced. Valid reasoning preserves the truth of premises. It does not say that from false premisses a true conclusion cannot be reached (by a multiple logically invalid steps).

## Why implication is true when p is false?

The implication p → q (read: p implies q, or if p then q) is the state- ment which asserts that if p is true, then q is also true. We agree that p → q is true when p is false. The statement p is called the hypothesis of the implication, and the statement q is called the conclusion of the implication.

## What false implies true?

The mistake is that we start from a false premise, that of 2=5 , and then use completely correct methods (multiply an equation on both sides by the same number) to arrive a true statement, that 0=0 . That process is logical: false can imply true.

## Is false == false true?

In Math a = b = c mean all a = b , b = c and a = c . So True is False == False means True == False and False == False and True == False , which is False . For boolean constants, is is equivalent to == . Actually, a is b == c only means (a is b) and (b == c) : a and c are not compared.