## Vacuously true

In logic,

statements of type if P, then Q are said to be vacuously true when the proposition P is false.
For example, the

statement, if sun rises in the north then everyone gets 100 percent in final exam, is a true

statement
since the proposition "sun rises in the north" is false.

The same idea can be extended in

universal quantification. If the restriction clause (where clause) in declaration
of

universal quantification cannot be true, then the quantification is said to be true regardless of truth value of
main assertions.
For example, the

statement

```
for all i: integer
where (i is even and i != 2 and i is prime)
there exists j:integer
j = 2 * i and j is prime
```

is vacuously true even if main assertion in the

statement is a mathematical contradiction.

Resources:

Reading contract
Wikipedia: Vacuous truth
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