Step 1: Evaluate each claim against the known clinical profile of lamotrigine, then keep the only one that holds up.
Step 2: Its pharmacokinetics give a half-life in the region of one day, which supports convenient dosing. That fact matches the 24 hour statement, so option (c) is sound.
Step 3: On efficacy in mood disorders, lamotrigine is well regarded for the depressive phase of bipolar illness, so saying it has reduced effect in depression is incorrect, eliminating (a).
Step 4: Ethosuximide and valproate dominate absence seizure therapy, leaving lamotrigine as a backup rather than first line, so (b) fails. Hepatic glucuronidation is its main clearance route, so the claim of no liver metabolism in (d) is also false.
\[\boxed{\text{t1/2 is about 24 hours}}\]