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Rockstar Games announces the next chapter in the hugely popular open-world action game series. Supergiant Games and Take-Two Interactive today announced the.Q:
Are the properties of a function $f$ of a function $g$ also properties of $g$?
I’m wondering if the following statement is true for a function $g$ and any function $f$:
$f$ has the property $P$ $\iff$ $g$ has the property $P$.
I’m aware that $P$ can be quantified in terms of predicates. However, I’m confused as to whether or not the universal quantifier (denoted by $\forall$) is treated the same way as the existential quantifier (denoted by $\exists$).
A:
It is true. To see this, assume $\forall x P(x)$ and $\forall x Q(x)$ where $P$ and $Q$ are both properties of $f$. Then $\forall x P(x) \iff \forall x Q(x)$, as follows from definition of $\forall$. Therefore $g$ has property $P$.
Bayard Thomas
San Francisco Chronicle
John Hitch (at left) and Billy Lyne spend time in the yard of their parents’ home in the Richmond District on Friday afternoon. Hitch and Lyne became the first siblings to be adopted into the same home as foster parents. The siblings are adopted by Patricia and Vincent Lento.
John Hitch (at left) and Billy Lyne spend time in the yard of their parents’ home in the Richmond District on Friday afternoon. Hitch and Lyne became the first siblings to be adopted into the same home as foster parents. The siblings are adopted by Patricia and Vincent Lento. (Bayard Thomas)
John Hitch (at left) and Billy Lyne spend time in the yard of their parents’ home in the Richmond District on Friday afternoon. Hitch and Lyne became the first siblings to be adopted into the same home as foster parents. The siblings are adopted by Patricia and Vincent Lento.
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