What is the set of all natural numbers N less than 5 in another​ way? Choose the correct answer below.

Question

A.StartSet x vertical line x is not an element of Upper N comma x less than or equals 5 EndSet
StartSet x vertical line x is not an element of Upper N comma x less than or equals 5 EndSet
B.StartSet x vertical line x is not an element of Upper N comma x less than 5 EndSet
StartSet x vertical line x is not an element of Upper N comma x less than 5 EndSet
C.StartSet x vertical line x is an element of Upper N comma x less than or equals 5 EndSet
StartSet x vertical line x is an element of Upper N comma x less than or equals 5 EndSet
D.StartSet x vertical line x is an element of Upper N comma x less than 5 EndSet
StartSet x vertical line x is an element of Upper N comma x less than 5 EndSet

Answer 1

To express the set of all natural numbers \( N \) that are less than 5, we need to consider the definition of natural numbers. Typically, natural numbers start from 1. Therefore, the natural numbers less than 5 are 1, 2, 3, and 4.

This can be expressed in set notation as:

\[ { x \mid x \in N, x < 5 } \]

Among the options provided, the correct one that represents this set is:

C. \({ x \mid x \text{ is an element of } N, x \leq 5 }\)

However, to specifically indicate numbers strictly less than 5, option D could be more aligned:

D. \({ x \mid x \text{ is an element of } N, x < 5 }\)

So the best answer would be D, which correctly states that \( x \) is a natural number less than 5.