Continue to solve

Jibu: $\boxed{\{3, 4\}}$

b) $A \cup B$

Jibu: $\boxed{\{1, 2, 3, 4, 5, 6\}}$

c) $A'$

Jibu: $\boxed{\{5, 6, 7\}}$

d) $B'$

Jibu: $\boxed{\{1, 2, 7\}}$

e) $A' \cap B'$

$A' = \{5, 6, 7\}$
$B' = \{1, 2, 7\}$

Jibu: $\boxed{\{7\}}$

f) $A' \cup B'$

$A' = \{5, 6, 7\}$
$B' = \{1, 2, 7\}$

Jibu: $\boxed{\{1, 2, 5, 6, 7\}}$

Swali la 17:
Kutokana na $\mu = \{a, b, c, d, e, f, g, h\}$, $A = \{a, b, c, d\}$, na $B = \{c, d, e, f\}$. Pata:

a) $A \cap B$

Jibu: $\boxed{\{c, d\}}$

b) $A \cup B$

Jibu: $\boxed{\{a, b, c, d, e, f\}}$

c) $A'$

Jibu: $\boxed{\{e, f, g, h\}}$

d) $B'$

Jibu: $\boxed{\{a, b, g, h\}}$

e) $A' \cap B'$

$A' = \{e, f, g, h\}$
$B' = \{a, b, g, h\}$

Jibu: $\boxed{\{g, h\}}$

f) $A' \cup B'$

$A' = \{e, f, g, h\}$
$B' = \{a, b, g, h\}$

Jibu: $\boxed{\{a, b, e, f, g, h\}}$

Swali la 18:
Kutokana na $\mu = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$, $A = \{1, 2, 3, 4, 5\}$, na $B = \{2, 4, 6, 8, 10\}$. Pata:

a) $A \cap B$

Jibu: $\boxed{\{2, 4\}}$

b) $A \cup B$

Jibu: $\boxed{\{1, 2, 3, 4, 5, 6, 8, 10\}}$

c) $A'$

Jibu: $\boxed{\{6, 7, 8, 9, 10\}}$

d) $B'$

Jibu: $\boxed{\{1, 3, 5, 7, 9\}}$

e) $A' \cap B'$

$A' = \{6, 7, 8, 9, 10\}$
$B' = \{1, 3, 5, 7, 9\}$

Jibu: $\boxed{\{7, 9\}}$

f) $A' \cup B'$

$A' = \{6, 7, 8, 9, 10\}$
$B' = \{1, 3, 5, 7, 9\}$

Jibu: $\boxed{\{1, 3, 5, 6, 7, 8, 9, 10\}}$

Swali la 19:
Kutokana na $\mu = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$, $A = \{1, 2, 3, 4, 5\}$, na $B = \{2, 4, 6, 8, 10\}$. Pata:

a) $n(A)$

Jibu: $\boxed{5}$

b) $n(B)$

Jibu: $\boxed{5}$

c) $n(A \cap B)$

$A \cap B = \{2, 4\}$

Jibu: $\boxed{2}$

d) $n(A \cup B)$

$A \cup B = \{1, 2, 3, 4, 5, 6, 8, 10\}$

Jibu: $\boxed{8}$

e) $n(A')$

$A' = \{6, 7, 8, 9, 10\}$

Jibu: $\boxed{5}$

f) $n(B')$

$B' = \{1, 3, 5, 7, 9\}$

Jibu: $\boxed{5}$

g) $n(A' \cap B')$

$A' \cap B' = \{7, 9\}$

Jibu: $\boxed{2}$

h) $n(A' \cup B')$

$A' \cup B' = \{1, 3, 5, 6, 7, 8, 9, 10\}$

Jibu: $\boxed{8}$

Swali la 20:
Kutokana na $\mu = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$, $A = \{1, 2, 3, 4, 5\}$, na $B = \{2, 4, 6, 8, 10\}$. Thibitisha kwamba:

a) $n(A \cup B) = n(A) + n(B) - n(A \cap B)$

$n(A \cup B) = 8$
$n(A) = 5$
$n(B) = 5$
$n(A \cap B) = 2$

Kauli ni Kweli.
Jibu: $\boxed{\text{Imethibitishwa}}$

b) $n(A \cup B)' = n(A' \cap B')$

Kwanza, $A \cup B = \{1, 2, 3, 4, 5, 6, 8, 10\}$.
$(A \cup B)' = \mu \setminus (A \cup B) = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \setminus \{1, 2, 3, 4, 5, 6, 8, 10\} = \{7, 9\}$.
$n((A \cup B)') = 2$.

Kutoka Swali la 19(g), $n(A' \cap B') = 2$.

Kauli ni Kweli. (Hii ni sheria ya De Morgan kwa idadi ya vipengele).
Jibu: $\boxed{\text{Imethibitishwa}}$

c) $n(A \cap B)' = n(A' \cup B')$

Kwanza, $A \cap B = \{2, 4\}$.
$(A \cap B)' = \mu \setminus (A \cap B) = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\} \setminus \{2, 4\} = \{1, 3, 5, 6, 7, 8, 9, 10\}$.
$n((A \cap B)') = 8$.

Kutoka Swali la 19(h), $n(A' \cup B') = 8$.

Kauli ni Kweli. (Hii ni sheria ya De Morgan kwa idadi ya vipengele).
Jibu: $\boxed{\text{Imethibitishwa}}$