Question

determine whether \\(\subseteq\\), \\(\subset\\), both, or neither can be placed in the blank to make the statement true.\\{r, t, m\\} ___ \\{r, t, m, c\\}choose the correct answer below.only \\(\subset\\)only \\(\subseteq\\)both \\(\subseteq\\) & \\(\subset\\)none of the above

Explanation:

Step1: Define subset symbols

• $\subseteq$ means "is a subset of": Every element of the first set is in the second set (includes equal sets).
• $\subset$ means "is a proper subset of": Every element of the first set is in the second set, and the second set has at least one element not in the first.

Step2: Compare the two sets

Set 1: $\{R, T, M\}$; Set 2: $\{R, T, M, C\}$
All elements of Set 1 are in Set 2, and Set 2 has an element $C$ not in Set 1.

Step3: Evaluate valid symbols

• $\{R, T, M\} \subseteq \{R, T, M, C\}$ is true (all elements match).
• $\{R, T, M\} \subset \{R, T, M, C\}$ is true (Set 2 has an extra element).

Answer:

Both $\subseteq$ & $\subset$