Final answer:
The claim that all of Beowulf's men stay by his side in battle with the dragon is false; only Wiglaf remains loyal. The provided statements about women's capabilities during war times are not directly related to Beowulf's story.
Step-by-step explanation:
When Beowulf goes into battle with the dragon, not all of his men stay by his side, which makes the statement False. In the epic poem, all but one of Beowulf's warriors flee in fear, failing to uphold the heroic code of loyalty to their leader in the face of danger. The one who remains is Wiglaf, who deems the act of abandoning their leader in his time of need to be shameful and unworthy of a true warrior.
The question pertaining to how women handled the burdens of war when their husbands and fathers went off to fight is a complex one. The answer provided as both 'a. True' and 'b. False' is not directly related to the context of Beowulf. However, it is worth noting that during war times in various historical contexts, women have often been capable of handling such burdens and have taken over roles and responsibilities traditionally held by men, which could render the statement False.