For each pair of statements, choose the one that is true: (a) {4} ∈ {4, 5} or 4 ∈ {4, 5} (b) {10, 12, 14} ⊆ {2, 4, 6, 8, ...} or {10, 12, 14} ∈ {2, 4, 6, 8, ...} (c) q ⊆ {q, r} or... For each pair of statements, choose the one that is true: (a) {4} ∈ {4, 5} or 4 ∈ {4, 5} (b) {10, 12, 14} ⊆ {2, 4, 6, 8, ...} or {10, 12, 14} ∈ {2, 4, 6, 8, ...} (c) q ⊆ {q, r} or {q} ⊆ {q, r} (d) {g} \( \nsim \) {e, f, h} or {g} ∈ {e, g, h} Read more

Steps to Solve

1. Analyze statement (a):

   • Option 1: ${4} \in {4, 5}$. This statement says the set containing 4 is an element of the set {4, 5}. This is false because the elements of {4, 5} are 4 and 5, not {4}.
   • Option 2: $4 \in {4, 5}$. This statement says that 4 is an element of the set {4, 5}, which is true.

2. Analyze statement (b):

   • Option 1: ${10, 12, 14} \subseteq {2, 4, 6, 8, ...}$. This statement means that the set {10, 12, 14} is a subset of the set of even numbers. Since 10, 12, and 14 are all even numbers, this is a valid subset. So, this statement is true.
   • Option 2: ${10, 12, 14} \in {2, 4, 6, 8, ...}$. This statement means {10, 12, 14} is an element of the set of even numbers. This is false.

3. Analyze statement (c):

   • Option 1: $q \subseteq {q, r}$. This is incorrect because $q$ is an element, not a set. Subsets relate two sets.
   • Option 2: ${q} \subseteq {q, r}$. This means the set containing q is a subset of the set {q, r}. Since q is an element of {q, r}, the set {q} is indeed a subset of {q, r}. So, this statement is true.

4. Analyze statement (d):

   • Option 1: ${g} \nsim {e, f, h}$. This uses the symbol $\nsim$, which the prompt says means non-equivalence. If it means the sets are not equal, then this is true because the set containing $g$ is not equal to the set containing $e$, $f$, and $h$.
   • Option 2: ${g} \in {e, g, h}$. This means the set {g} is an element of the set {e, g, h}. The elements of {e, g, h} are e, g, and h. This statement is thus false.