Question

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

Explanation:

: $5 \subseteq \{4, 5, 6\}$ is wrong (element vs set). Wait, the first option: $5
subseteq \{4, 6, 7\}$ – even though the notation is off, the idea is $5$ is not in $\{4, 6, 7\}$? Wait, no, $\{4, 6, 7\}$ has elements $4,6,7$, so $5
otin \{4, 6, 7\}$, but the symbol $
subseteq$ is for sets. Wait, maybe the first option is $5
otin \{4, 6, 7\}$ (written as $5
subseteq$ by mistake). Then $5
otin \{4, 6, 7\}$ is true? Wait, no, the second option: $5 \subseteq \{4, 5, 6\}$ is wrong (element vs set). Wait, maybe the first option is correct in the sense that $5$ is not a subset (since it's an element), but the notation is incorrect. But the second option is definitely wrong (element can't be a subset). So the first option (despite notation) is the "true" one here, but likely a typo. But let's re - check:

Wait, the first option in (d) is $5
subseteq \{4, 6, 7\}$ – since $5$ is an element, not a set, the subset relation is inapplicable, but the idea is $5$ is not in $\{4, 6, 7\}$, so the statement $5
subseteq \{4, 6, 7\}$ (even with wrong symbol) is "true" in the sense that $5$ is not a subset (because it's not a set) and also not in the set. The second option: $5 \subseteq \{4, 5, 6\}$ is false because $5$ is an element, not a set. So the first option is the true one here (assuming $
subseteq$ is a typo for $
otin$).

Now, summarizing the true statements for each part:

(a) $m \in \{m, r\}$

(b) $\{9, 11, 13\} \subseteq \{1, 3, 5, 7, \dots\}$

(c) $\{h\} \subseteq \{h, k\}$

(d) $5
subseteq \{4, 6, 7\}$ (assuming notation error, as $5$ is not in $\{4, 6, 7\}$ and not a subset)

If we have to choose the true one for each pair:

(a) The true one is $m \in \{m, r\}$

(b) The true one is $\{9, 11, 13\} \subseteq \{1, 3, 5, 7, \dots\}$

(c) The true one is $\{h\} \subseteq \{h, k\}$

(d) The true one is $5
subseteq \{4, 6, 7\}$ (or $5
otin \{4, 6, 7\}$ if it's a typo)

Answer:

: $5 \subseteq \{4, 5, 6\}$ is wrong (element vs set). Wait, the first option: $5
subseteq \{4, 6, 7\}$ – even though the notation is off, the idea is $5$ is not in $\{4, 6, 7\}$? Wait, no, $\{4, 6, 7\}$ has elements $4,6,7$, so $5
otin \{4, 6, 7\}$, but the symbol $
subseteq$ is for sets. Wait, maybe the first option is $5
otin \{4, 6, 7\}$ (written as $5
subseteq$ by mistake). Then $5
otin \{4, 6, 7\}$ is true? Wait, no, the second option: $5 \subseteq \{4, 5, 6\}$ is wrong (element vs set). Wait, maybe the first option is correct in the sense that $5$ is not a subset (since it's an element), but the notation is incorrect. But the second option is definitely wrong (element can't be a subset). So the first option (despite notation) is the "true" one here, but likely a typo. But let's re - check:

Wait, the first option in (d) is $5
subseteq \{4, 6, 7\}$ – since $5$ is an element, not a set, the subset relation is inapplicable, but the idea is $5$ is not in $\{4, 6, 7\}$, so the statement $5
subseteq \{4, 6, 7\}$ (even with wrong symbol) is "true" in the sense that $5$ is not a subset (because it's not a set) and also not in the set. The second option: $5 \subseteq \{4, 5, 6\}$ is false because $5$ is an element, not a set. So the first option is the true one here (assuming $
subseteq$ is a typo for $
otin$).

Now, summarizing the true statements for each part:

(a) $m \in \{m, r\}$

(b) $\{9, 11, 13\} \subseteq \{1, 3, 5, 7, \dots\}$

(c) $\{h\} \subseteq \{h, k\}$

(d) $5
subseteq \{4, 6, 7\}$ (assuming notation error, as $5$ is not in $\{4, 6, 7\}$ and not a subset)

If we have to choose the true one for each pair:

(a) The true one is $m \in \{m, r\}$

(b) The true one is $\{9, 11, 13\} \subseteq \{1, 3, 5, 7, \dots\}$

(c) The true one is $\{h\} \subseteq \{h, k\}$

(d) The true one is $5
subseteq \{4, 6, 7\}$ (or $5
otin \{4, 6, 7\}$ if it's a typo)