Put '+' or '=' in the spaces provided: Equivalent sets have the same number of elements (cardinality). Equal sets have exactly the same elements. a. 2, 4, 6, 8, 10 _ 1, 3, 5, 7, 9 b. Ada, Shola, Ugo,

Here are the solutions to the problems:

2. Put '+' or '=' in the spaces provided.

• Equivalent sets have the same number of elements (cardinality).
• Equal sets have exactly the same elements.

a. $\{2, 4, 6, 8, 10\}$ has 5 elements. $\{1, 3, 5, 7, 9\}$ has 5 elements. The elements are different, but the number of elements is the same. * $\{2, 4, 6, 8, 10\}$ + $\{1, 3, 5, 7, 9\}$

b. $\{$Ada, Shola, Ugo, Musa$\}$ has 4 elements. $\{$Shola, Musa, Ugo, Ada$\}$ has 4 elements. The elements are the same, just in a different order. * $\{$Ada, Shola, Ugo, Musa$\}$ = $\{$Shola, Musa, Ugo, Ada$\}$

c. $\{5, 6, 5, 7\}$ simplifies to $\{5, 6, 7\}$ (3 unique elements). $\{7, 5, 7, 6\}$ simplifies to $\{7, 5, 6\}$ (3 unique elements). The elements are the same. * $\{5, 6, 5, 7\}$ = $\{7, 5, 7, 6\}$

d. $\{a, 3, u, f, 9\}$ has 5 elements. $\{a, f, u, 9, 3\}$ has 5 elements. The elements are the same, just in a different order. * $\{a, 3, u, f, 9\}$ = $\{a, f, u, 9, 3\}$

e. $\{a, 3, a\}$ simplifies to $\{a, 3\}$ (2 unique elements). $\{a, 3\}$ has 2 elements. The elements are the same. * $\{a, 3, a\}$ = $\{a, 3\}$

f. The first set (parallelogram) contains $\{a, b, c, d, 1, 4, 7, 9, 11, 13, 5, 8\}$. It has 12 unique elements.
The second set (circle) contains $\{e, f, g, h, 2, 3, 6, 10, 11, 13, 5, 8\}$. It has 12 unique elements.
The number of elements is the same, but the elements are different. * +

3. Which of these sets are equal?

• Equal sets have exactly the same elements.

a.

• $A = \{r, t, s\}$
• $B = \{s, r, s, t\}$ simplifies to $\{s, r, t\}$
• $C = \{t, r, s, t\}$ simplifies to $\{t, r, s\}$
• $D = \{r, r, r, s, t\}$ simplifies to $\{r, s, t\}$ All sets contain the same unique elements $\{r, s, t\}$. Therefore, A, B, C, and D are all equal.

b.

• (i) $A = \{x \mid x \text{ is a letter in the word "follow"}\}$ The unique letters in "follow" are $\{f, o, l, w\}$. So, $A = \{f, o, l, w\}$.
• (ii) $B = \text{The letters which appear in the word "wolf"}$ The unique letters in "wolf" are $\{w, o, l, f\}$. So, $B = \{w, o, l, f\}$.
• (iii) $C = \{x \mid x \text{ is a letter in the word "flow"}\}$ The unique letters in "flow" are $\{f, l, o, w\}$. So, $C = \{f, l, o, w\}$.
• (iv) $D = \text{the letters } f, l, o, w.$ So, $D = \{f, l, o, w\}$. All sets contain the same unique elements $\{f, l, o, w\}$. Therefore, A, B, C, and D are all equal.

Which of these sets are equivalent?

• Equivalent sets have the same number of elements (cardinality).

a.

• $A = \{1, 3, 4, 5\}$. Cardinality $|A|=4$.
• $B = \{a, a, b, c, d\}$ simplifies to $\{a, b, c, d\}$. Cardinality $|B|=4$.
• $C = \{3, 4, 1, 2\}$. Cardinality $|C|=4$.
• $D = \{e, f, g, h\}$. Cardinality $|D|=4$.
• $E = \{3, 1, 3, 4, 5\}$ simplifies to $\{3, 1, 4, 5\}$. Cardinality $|E|=4$. All sets have a cardinality of 4. Therefore, A, B, C, D, and E are all equivalent.

b.

• $A = \{x \mid x \text{ is a letter in the word "adore"}\}$ The unique letters in "adore" are $\{a, d, o, r, e\}$. Cardinality $|A|=5$.
• $B = \text{The letters which appear in the word "arode"}$ The unique letters in "arode" are $\{a, r, o, d, e\}$. Cardinality $|B|=5$.
• $C = \{x \mid x \text{ is a letter in the word "radoe"}\}$ The unique letters in "radoe" are $\{r, a, d, o, e\}$. Cardinality $|C|=5$. All sets have a cardinality of 5. Therefore, A, B, and C are all equivalent.