Final answer:
Sets are represented using curly braces enclosing the elements. For the months with 'N', the set is {January, June, November}. Hexadecimal characters form the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}. Letters in 'taradiddle' are represented by the set {a, d, e, i, l, r, t}.
Step-by-step explanation:
Representing sets using set notation involves identifying the elements that belong to the set and enclosing them within curly braces. Here are the set notations for the given problems:
Set of the months of the year whose name contains the letter N:
The months of the year that contain the letter 'N' are January, June, and November. Thus, the set can be represented as {January, June, November}.
Set of hexadecimal characters:
Hexadecimal characters include the digits 0 to 9 and the letters A to F. The set of hexadecimal characters is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F}.
Set of letters in the word 'taradiddle':
The word 'taradiddle' contains the letters a, d, e, i, l, r, and t. The set notation for the letters in the word 'taradiddle' is {a, d, e, i, l, r, t}.
Remember that in mathematics, symbols used in equations and set notation are placeholders that represent elements within a given context. When constructing sets, it's important to carefully consider which elements are included based on the criteria specified in the problem.