1. The problem states that we have three sets $A$, $B$, and $K$ such that $A \subset K$, $B \subset K$, and $A \cap B = \emptyset$. 2. This means both $A$ and $B$ are subsets of $K$, and they do not share any elements (their intersection is empty). 3. The Venn diagram would show $K$ as a large set containing both $A$ and $B$ as two separate, non-overlapping subsets inside it. 4. Next, we are given four numbers: $2.6$, $\frac{4}{17}$, $\sqrt{12}$, and $\sqrt{\frac{112}{7}}$. 5. We need to place these numbers in the Venn diagram of Rational numbers (outer circle) and Integers (inner circle). 6. Recall: - Integers are whole numbers (positive, negative, zero) without fractions or decimals. - Rational numbers are numbers that can be expressed as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q \neq 0$. 7. Analyze each number: - $2.6$ is a decimal, not an integer, but it can be expressed as $\frac{26}{10}$, so it is rational but not integer. - $\frac{4}{17}$ is a fraction of integers, so rational but not integer. - $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$, which is irrational (since $\sqrt{3}$ is irrational), so it is not rational. - $\sqrt{\frac{112}{7}} = \sqrt{16} = 4$, which is an integer. 8. Placement: - $4$ (from $\sqrt{\frac{112}{7}}$) goes inside the Integers circle. - $2.6$ and $\frac{4}{17}$ go in the Rational numbers circle but outside the Integers circle. - $\sqrt{12}$ goes outside both circles (irrational). Final answer: - Integers: $4$ - Rational but not integer: $2.6$, $\frac{4}{17}$ - Neither rational nor integer: $\sqrt{12}$