1. The problem asks to identify the correct interval or set relation for each question. 2. For question 11: $\mathbb{R}$ is the set of all real numbers, which corresponds to the interval $]-\infty, \infty[$. So the answer is (b). 3. For question 12: Check if $-3$ belongs to the interval $]-4,1]$. Since $-3$ is greater than $-4$ and less than or equal to $1$, $-3 \in ]-4,1]$. So the answer is (a). 4. For question 13: $\mathbb{R}$ is the set of all real numbers, and $]0,\infty[$ is the set of positive real numbers. Since $\mathbb{R}$ contains numbers not in $]0,\infty[$, $\mathbb{R} \not\subset ]0,\infty[$. So the answer is (d). 5. For question 14: The intersection $[4,9] \cap [7,10]$ is the set of numbers common to both intervals, which is $[7,9]$. So the answer is (d). 6. For question 15: If $a \in ]2,5[$, then $a$ is strictly between 2 and 5, so it cannot be equal to 2 or 5, but can be 4. So the answer is (c). 7. For question 16: The union $]-3,5] \cup ]2,7]$ covers from just greater than $-3$ up to 7, so it is $]-3,7]$. So the answer is (b). 8. For question 17: If $X = ]-\infty,3[$, then the complement $\overline{X}$ is $[3,\infty[$. So the answer is (c). 9. For question 18: The difference $]0,5[ - ]3,7[$ removes from $]0,5[$ the part overlapping with $]3,7[$, leaving $]0,3]$. So the answer is (a). 10. For question 19: The intersection $]-1,1[ \cap \{1,0,-1\}$ includes only elements of the set inside the interval. Since $0$ is inside $]-1,1[$ but $1$ and $-1$ are not (interval is open), the intersection is $\{0\}$. So the answer is (d). 11. For question 20: The difference $]2,5[ - \{2,5\}$ removes the points 2 and 5 from the open interval $]2,5[$, but since 2 and 5 are not in the open interval, the set remains $]2,5[$. So the answer is (c). 12. For question 21: The intersection $\mathbb{R} \cap ]2,5[$ is $]2,5[$ since $]2,5[$ is a subset of $\mathbb{R}$. So the answer is (d).