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Claim. P. Borg, On Chvátal's conjecture and a conjecture on families of signed sets, European J. Combin. 32 (2011), no. 1, 140--145, proposes a weighted version of Chvátal's conjecture, the corrected Statement of Problem 701, and proves the weighted version for weighted families having a dominant element, as the zbMATH review of the paper (Zbl 1207.05002) states the result. Unit weights are a special case, so the corrected Statement holds for every family with a dominant element in the paper's sense.
Covers. Families closed under taking subsets that have a dominant element, in the sense of the paper. The paper's other conjecture, on families of signed sets, is not part of the problem.
Acceptance. Refereed: European J. Combin. 32 (2011), no. 1, 140--145. The site's curator credits the result, but the site labels the problem OPEN, so no review is listed.