Given U = 16, 17, 18, 19, 20, 21, 22, x = x: x < 20, and Y = y: 17 ≤ y ≤ 21. Find: a) X ∩ Y, b) X ∪ Y, c) X ∩ Y, d) Represent X, Y and U on a Venn diagram.

This part is a duplicate of part b) in the question.

A Venn diagram for these sets would consist of a rectangle representing the universal set $U$, and two overlapping circles representing sets $X$ and $Y$.

The elements would be placed in the following regions:

• Intersection ($X \cap Y$): Elements common to both $X$ and $Y$. $X \cap Y = \{16, 17, 18, 19\} \cap \{17, 18, 19, 20, 21\} = \{17, 18, 19\}$ These elements go in the overlapping region of the circles.
• Only $X$ ($X \setminus Y$): Elements in $X$ but not in $Y$. $X \setminus Y = \{16\}$ This element goes in the part of circle $X$ that does not overlap with $Y$.
• Only $Y$ ($Y \setminus X$): Elements in $Y$ but not in $X$. $Y \setminus X = \{20, 21\}$ These elements go in the part of circle $Y$ that does not overlap with $X$.
• Outside $X$ and $Y$ ($(X \cup Y)'$): Elements in $U$ but not in $X$ or $Y$. $X \cup Y = \{16, 17, 18, 19, 20, 21\}$ $(X \cup Y)' = U \setminus (X \cup Y) = \{22\}$ This element goes inside the rectangle but outside both circles.