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.


Reading contract
Wikipedia: Vacuous truth

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