It looks like the image contains a mathematical activity involving propositional logic. Here's a summary of the main tasks:

Activity Overview:

1. Determine the truth value of the following propositional functions:

   • P(x): x is an integer.
   • Q(x): x is a multiple of 5.
   • R(x): x is greater than 2.
   • S(x): x is less than or equal to 6.

   Then, evaluate various logical operations involving these propositions.

2. Evaluate the truth values of specific expressions given some values for x, like:

   • $A) \, x \in \mathbb{E}, x^2 = 32$
   • $B) \, x \in \mathbb{E}, x^2 = 19$
   • $C) \, x \in \mathbb{E}, x = 16$

3. Apply set notation and functions to convert propositional functions into logical propositions.

Further Explanation:

• The expressions involve checking if a number satisfies certain conditions (e.g., being an integer, being a multiple of 5, etc.).
• You are also tasked with finding the truth values for specific propositions, such as $x^2 = 32$ or $x^2 = 19$, under certain assumptions about $x$.

Would you like me to help you solve any of these problems step by step? Or do you have a specific question regarding any part of this?