The best choice to fill in the blank is "D. concede any ground," as it indicates that both sides in the debate refuse to give up any part of their argument. This aligns with the description of a heated argument. Each side believes strongly in their position, exemplifying intransigence in their viewpoints.
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In the sentence provided, we are tasked with selecting the best word or phrase to complete the blank, considering the context of a debate where both sides are firmly convinced of their own arguments.
Let's evaluate each option:
(A) share their points : This option suggests that both sides share their arguments, but the sentence hints at a lack of agreement or compromise, making this option less suitable.
(B) argue persuasively : Although both sides are attempting to argue persuasively, this option does not capture the sense of refusal implied in the sentence's context.
(C) ignore the topic : Ignoring the topic would mean not engaging in a debate at all, which contradicts the description of a 'heated' debate.
(D) concede any ground : This option accurately reflects the situation where both sides are stubbornly holding their positions without giving any leeway.
Therefore, the most fitting option is (D) concede any ground because it conveys the idea that both sides are so convinced of their correctness that they are unwilling to acknowledge any merit in the opposing position or to compromise in any form. This is a common situation in debates, especially heated ones, where participants are strongly attached to their views.
The sentence, completed, would read: "The debate grew heated as both sides refused to concede any ground, each convinced of their position's absolute validity."