## 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.

## Which statement about the logical operators & and && is true?

Remarks. The logical AND operator ( && ) **returns true if both operands are true** and returns false otherwise. The operands are implicitly converted to type bool before evaluation, and the result is of type bool . Logical AND has left-to-right associativity.

## What is Boolean true or false?

In computer science, a Boolean is **a logical data type that can have only the values true or false** .