Denial of Universality/Examples/x less than or equal to 3/Examples
Jump to navigation
Jump to search
Examples of Denial of Universality: $\forall x \in S: x \le 3$
Example where $S = \set {2, 3, 4}$
Let $P$ be the statement:
- $\forall x \in S: x \le 3$
and $\lnot P$ its negation:
- $\exists x \in S: x > 3$
Let $S = \set {2, 3, 4}$.
Then we have that:
- $P$ is false
and consequently:
- $\lnot P$ is true
Example where $S = \closedint 0 3$
Let $P$ be the statement:
- $\forall x \in S: x \le 3$
and $\lnot P$ its negation:
- $\exists x \in S: x > 3$
Let $S = \closedint 0 3$ where $\closedint \cdot \cdot$ denotes a closed real interval.
Then we have that:
- $P$ is true
and consequently:
- $\lnot P$ is false