Some 202204281244 can express both property of #202204281245 and #202205062055 which make it a #202205061208, named Universal Conditional Statement.
For example: For all computers, if it is a laptop, then it has operating system on it. This statement has first the universal property (for all), then the conditional property (if-then). It is a Universal Conditional Statement. The statement could be further transformed which means the same thing, shown as follows:
- For all computer \(c\), if \(c\) is a laptop, then \(c\) has operating system on it.
- For all laptop \(c\), \(c\) has operating system on it. (explicit universal)
- If \(c\) is a laptop, then \(c\) has an operating system on it. (explicit conditional)
The negation of it is expressed formally as \(\sim (\forall x, P(x) \rightarrow Q(x)) \equiv \exists x \text{ such that } P(x) \land \sim Q(x)\). Consider the statement “For all computer programs, if it is in Java programming language, then it at least has 5 lines”. Transform to its negated form, that is an 202204281254 that consists of an and statement which could be referred to the section of Conditional Statement in 202205061240#, which is “There exists at least one computer program that it is in Java programming language, and it has less than 5 lines”.