The correct word to complete the sentence is "essential". Therefore, the sentence reads: "Nutritionists have long emphasized the importance of a balanced diet, which is essential, emphasizing that intake of nutrients can significantly improve overall health and vitality."
The identity element in an operation table is the element which, when operated on any element of the set, leaves it unchanged. To determine the identity element, we look for an element in the table such that its row and column are identical to the headers of the table. From the given table, we are looking for a row and a column where all the elements match the top header (for the column) and the side header (for the row). Examine each row and column for the pattern where the values match the headers: {w, x, y, z}. Starting with the first row, we see that the element "w" has the row {w, x, y, z}, which matches the header exactly. This indicates that "w" acts as the identity element because w*w = w, w*x = x, w*y = y, and w*z = z. Therefore, the identity element under the operation table is "w". The correct answer is: A) w
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