Question

for each pair of statements, choose the one that is true. (a) $\circ \\{m\\} \in \\{m, r\\}$ $\circ m \in \\{m, r\\}$ (b) $\circ \\{9, 11, 13\\} \in \\{1, 3, 5, 7, \ldots\\}$ $\circ \\{9, 11, 13\\} \subseteq \\{1, 3, 5, 7, \ldots\\}$ (c) $\circ h \subseteq \\{h, k\\}$ $\circ \\{h\\} \subseteq \\{h, k\\}$ (d) $\circ 5 \
ot\in \\{4, 6, 7\\}$ $\circ 5 \subseteq \\{4, 5, 6\\}$

Explanation:

Step1: Analyze set membership (a)

$\{m\}$ is a set, not an element of $\{m, r\}$; $m$ is an element, so $m \in \{m, r\}$ is true.

Step2: Analyze set relation (b)

$\{9,11,13\}$ is not an element of the odd number set, but all its elements are odd numbers, so $\{9, 11, 13\} \subseteq \{1, 3, 5, 7, ...\}$ is true.

Step3: Analyze subset relation (c)

$h$ is an element, not a set, so cannot be a subset; $\{h\}$ is a set whose element is in $\{h,k\}$, so $\{h\} \subseteq \{h, k\}$ is true.

Step4: Analyze membership/subset (d)

$5$ is an element, not a set, so cannot be a subset; $5$ is not in $\{4,6,7\}$, so $5
otin \{4, 6, 7\}$ is true.

Answer:

(a) $m \in \{m, r\}$
(b) $\{9, 11, 13\} \subseteq \{1, 3, 5, 7, ...\}$
(c) $\{h\} \subseteq \{h, k\}$
(d) $5
otin \{4, 6, 7\}$