In the Venn diagram below, U is the universal set and M and N are subsets of U. Use the Venn diagram to answer the following questions: list the elements of NUM ii (MnN)' iii NInm

Here are the elements for Question 1, based on the Venn diagram:

Question 1: List the elements of:

• i. $N \cup M$ This represents the union of set $N$ and set $M$, which includes all elements present in either $N$ or $M$ or both. From the diagram: $N = \{f, e, g, a, r, c\}$ $M = \{h, t, a, r, c\}$

  $$N \cup M = \boxed{\{a, c, e, f, g, h, r, t\}}$$

• ii. $(M \cap N)'$ First, find the intersection of $M$ and $N$, which are the elements common to both sets. $M \cap N = \{a, r, c\}$ Then, find the complement of $(M \cap N)$, which includes all elements in the universal set $U$ that are not in $(M \cap N)$. The universal set $U = \{a, b, c, d, e, f, g, h, r, t, w\}$.

  $$(M \cap N)' = U \setminus \{a, r, c\} = \boxed{\{b, d, e, f, g, h, t, w\}}$$

• iii. $N \cap M'$ This represents the elements that are in set $N$ but not in set $M$. Elements in $N$: $\{f, e, g, a, r, c\}$ Elements in $M$: $\{h, t, a, r, c\}$

  $$N \cap M' = \boxed{\{e, f, g\}}$$

• iv. $M \setminus N$ This represents the elements that are in set $M$ but not in set $N$. Elements in $M$: $\{h, t, a, r, c\}$ Elements in $N$: $\{f, e, g, a, r, c\}$

  $$M \setminus N = \boxed{\{h, t\}}$$

• v. $U$ This represents the universal set, which includes all elements shown in the diagram.

  $$U = \boxed{\{a, b, c, d, e, f, g, h, r, t, w\}}$$