Questions: Here are the meanings of some of the symbols that appear in the statements below. - C means "is a subset of." - C means "is a proper subset of." - £ means "is not a subset of." - ∅ is the empty set. For each statement, decide if it is true or false. (a) 11,15 ⊆ 11,12,13,14,15 True False (b) 2,4,9 ⊆ ∅ True False (c) c, d, f, g ⊂ c, f True False (d) t, u, z ⫌ t, u, z True False

Here are the meanings of some of the symbols that appear in the statements below.
- C means "is a subset of."
- C means "is a proper subset of."
- £ means "is not a subset of."
- ∅ is the empty set.

For each statement, decide if it is true or false.
(a) 11,15 ⊆ 11,12,13,14,15
True False
(b) 2,4,9 ⊆ ∅
True False
(c) c, d, f, g ⊂ c, f
True False
(d) t, u, z ⫌ t, u, z
True False

Transcript text: Here are the meanings of some of the symbols that appear in the statements below. - C means "is a subset of." - C means "is a proper subset of." - $£$ means "is not a subset of." - $\varnothing$ is the empty set. For each statement, decide if it is true or false. (a) $\{11,15\} \subseteq\{11,12,13,14,15\}$ True False (b) $\{2,4,9\} \subseteq \varnothing$ True False (c) $\{c, d, f, g\} \subset\{c, f\}$ True False (d) $\{t, u, z\} \nsucceq\{t, u, z\}$ True False

Solution

Solution Steps

To determine the truth value of each statement, we need to check the relationships between the sets as described by the symbols.

(a) Check if the set {11, 15} is a subset of {11, 12, 13, 14, 15}. (b) Check if the set {2, 4, 9} is a subset of the empty set. (c) Check if the set {c, d, f, g} is a proper subset of {c, f}. (d) Check if the set {t, u, z} is not a subset of {t, u, z}.

Step 1: Evaluate Statement (a)

We check if $ \{11, 15\} \subseteq \{11, 12, 13, 14, 15\} $. Since both elements $ 11 $ and $ 15 $ are present in the second set, this statement is true. Thus, $ (a) $ is True.

Step 2: Evaluate Statement (b)

We check if $ \{2, 4, 9\} \subseteq \varnothing $. The empty set contains no elements, so it cannot contain any non-empty set. Therefore, this statement is false. Thus, $ (b) $ is False.

Step 3: Evaluate Statement (c)

We check if $ \{c, d, f, g\} \subset \{c, f\} $. A proper subset must have at least one element not in the other set, and since $ d $ and $ g $ are not in $ \{c, f\} $, this statement is false. Thus, $ (c) $ is False.

Step 4: Evaluate Statement (d)

We check if $ \{t, u, z\} \nsucceq \{t, u, z\} $. Since both sets are identical, the first set is indeed a subset of the second set, making this statement false. Thus, $ (d) $ is False.