Let's analyze each pair of sets to determine if they are equal:

(a) $P = \{ \text{vowels in the word SCIENCE} \}$ and $Q = \{A, I, E\}$

• Set $P$: The vowels in "SCIENCE" are $\{ I, E \}$ (no "A").
• Set $Q$: Given as $\{ A, I, E \}$.

Since $P = \{ I, E \}$ and $Q = \{ A, I, E \}$, they are not equal because $A$ is in $Q$ but not in $P$.

(b) $M = \{ x : 7 \leq x \leq 18, x \text{ is an even number} \}$ and $N = \{ 8, 10, 12, 14, 16, 18 \}$

• Set $M$: All even numbers between 7 and 18 inclusive are $\{ 8, 10, 12, 14, 16, 18 \}$.
• Set $N$: Given directly as $\{ 8, 10, 12, 14, 16, 18 \}$.

Since both $M$ and $N$ contain exactly the same elements, they are equal.

(c) $V = \{ \text{multiples of 4 less than 20} \}$ and $W = \{ 4, 8, 12, 16 \}$

• Set $V$: Multiples of 4 under 20 are $\{ 4, 8, 12, 16 \}$.
• Set $W$: Given directly as $\{ 4, 8, 12, 16 \}$.

Since both $V$ and $W$ contain exactly the same elements, they are equal.

(d) $C = \{ \text{even numbers between 13 and 20} \}$ and $D = \{ \text{factors of 12} \}$

• Set $C$: Even numbers between 13 and 20 are $\{ 14, 16, 18 \}$.
• Set $D$: Factors of 12 are $\{ 1, 2, 3, 4, 6, 12 \}$.

Since $C$ and $D$ do not contain any common elements, they are not equal.

Summary of Results:

1. (a) Not Equal
2. (b) Equal
3. (c) Equal
4. (d) Not Equal

Would you like further explanation on any of these results?

Here are some related questions for further practice:

1. Can you find the intersection of sets $P$ and $Q$ from part (a)?
2. What would be the union of sets $M$ and $N$ in part (b)?
3. How would you describe the difference between sets $V$ and $W$ from part (c)?
4. What is the complement of set $C$ within the set of even numbers less than 20?
5. Can you identify any subsets within sets $C$ and $D$ in part (d)?

Tip: When comparing sets, always check each element to confirm if they match entirely. Sets are only equal if they have exactly the same elements.