1. **Stating the problem:** We have three variables: $u$, $x$, and $y$. The conditions are: - $u$ is a natural number less than 20. - $x$ is a prime number. - $y = x$. - $5 < y < 15$. - $y$ and $u$ are subsets (likely meaning sets or values related). 2. **Understanding the problem:** We want to find values of $u$, $x$, and $y$ that satisfy these conditions. 3. **Step 1: Identify possible values for $x$ and $y$ given $5 < y < 15$ and $y = x$:** Since $x$ is prime and $y = x$, $y$ must be a prime number between 5 and 15. The prime numbers less than 20 are: 2, 3, 5, 7, 11, 13, 17, 19. From these, primes between 5 and 15 are: 7, 11, 13. So possible values for $x$ and $y$ are $7$, $11$, or $13$. 4. **Step 2: Identify possible values for $u$:** $u$ is a natural number less than 20, so $u \\in \{1, 2, 3, ..., 19\}$. 5. **Step 3: Interpretation of "$y$ and $u$ are subset":** If $y$ and $u$ are sets, then $y$ and $u$ could be subsets of some universal set. Since $y$ is a single number equal to $x$, and $u$ is a natural number, this might mean $\{y\} \subseteq \{u\}$ or vice versa. Since $u$ is a number, the most reasonable interpretation is that $u$ is a set of natural numbers less than 20, and $y$ is an element of $u$. 6. **Final conclusion:** - $x = y$ is one of $7$, $11$, or $13$. - $u$ is a subset of natural numbers less than 20 that contains $y$. **Example:** - Let $y = 7$. - Then $u$ can be any subset of $\{1, 2, ..., 19\}$ that includes $7$. This satisfies all conditions. **Summary:** $$x = y \in \{7, 11, 13\}$$ $$u \subseteq \{1, 2, ..., 19\} \text{ and } y \in u$$