Represent the following sets (a) \( \{x: x \leq 7 ; x \in \mathbb{Z}\} \) (c) \( \{x: x<7 ; x \in \mathbb{N}\} \) (c) \( \{x:-34 \frac{1}{2} ; x \in \mathbb{R}\right\} \)

For the first set, we are considering all integers less than or equal to 7. This set can be represented as: \( \{..., -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7\} \). The second set is for natural numbers (positive integers) that are less than 7, which includes: \( \{1, 2, 3, 4, 5, 6\} \). For the third set with integers between -3 and 1, inclusive on the right side, we have: \( \{-2, -1, 0, 1\} \). The fourth set includes all non-negative natural numbers (including 0) that are less than 12: \( \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\} \). For the set containing real numbers between -3 and 1 (where -3 is excluded and 1 is included), we can represent this as: \( (-3, 1] \). Lastly, the set of real numbers greater than \( 4\frac{1}{2} \) (or 4.5) is shown as: \( (4.5, \infty) \).