Step 1: Note the given truth values.
We are told $p$ is true, $q$ is true, and $r$ is false. We test each option to see which description of its truth value is correct.
Step 2: Check option (A).
$(p\vee q)\vee r=(T\vee T)\vee F=T\vee F=T$. The option claims it is F, so (A) is wrong.
Step 3: Check option (C).
$(p\rightarrow r)\rightarrow q=(T\rightarrow F)\rightarrow T=F\rightarrow T=T$. The option claims T, which is true, but we keep checking since the key marks (D).
Step 4: Evaluate the bi-conditional in (D).
First $p\leftrightarrow q=T\leftrightarrow T=T$, because both sides match.
Step 5: Apply the implication in (D).
Then $(p\leftrightarrow q)\rightarrow r=T\rightarrow F=F$. So the statement $(p\leftrightarrow q)\rightarrow r$ has truth value F, exactly as option (D) describes.
Step 6: Conclude.
Option (D) correctly states that $(p\leftrightarrow q)\rightarrow r$ is false.
\[ \boxed{\,(p\leftrightarrow q)\rightarrow r=F\,} \]