Questions: For each statement, decide if it is true or false. (a) f, g, k ⊂ f, g, k True False (b) 2,4 ∈ 1,2,3,4, ... True False (c) p, q, r, s, t, u ⊆ p, s, u True False (d) ∅ ⊆ 14,18 True False

Transcript text: For each statement, decide if it is true or false. (a) $\{f, g, k\} \subset\{f, g, k\}$ True False (b) $\{2,4\} \in\{1,2,3,4, \ldots\}$ True False (c) $\{p, q, r, s, t, u\} \subseteq\{p, s, u\}$ True False (d) $\varnothing \subseteq\{14,18\}$ True False

Solution

Solution Steps

To determine if each statement is true or false, we need to understand the concepts of subset and element membership in sets.

(a) A set is always a subset of itself. (b) Check if the set {2,4} is an element of the set of natural numbers. (c) Check if the set {p, q, r, s, t, u} is a subset of {p, s, u}. (d) The empty set is a subset of any set.

Step 1: Check if $\{f, g, k\} \subset \{f, g, k\}$

A set is always a subset of itself. Therefore, $\{f, g, k\} \subset \{f, g, k\}$ is true.

Step 2: Check if $\{2, 4\} \in \{1, 2, 3, 4, \ldots\}$

The set $\{2, 4\}$ is not an element of the set of natural numbers $\{1, 2, 3, 4, \ldots\}$. Therefore, $\{2, 4\} \in \{1, 2, 3, 4, \ldots\}$ is false.

Step 3: Check if $\{p, q, r, s, t, u\} \subseteq \{p, s, u\}$

The set $\{p, q, r, s, t, u\}$ is not a subset of $\{p, s, u\}$ because it contains elements (q, r, t) that are not in $\{p, s, u\}$. Therefore, $\{p, q, r, s, t, u\} \subseteq \{p, s, u\}$ is false.

Step 4: Check if $\varnothing \subseteq \{14, 18\}$

The empty set $\varnothing$ is a subset of any set. Therefore, $\varnothing \subseteq \{14, 18\}$ is true.