Problem

Determine whether $\subseteq, C$, both, or neither can be placed in the blank to make the statement true. $1 \leftarrow$ \[ \{T, M, C\}-\{T, M, C, R\} \] Choose the correct answer below. Only C Only $\subseteq$ Both $\subseteq \& \subset$ None of the above

Solution

Step 1 :The problem is asking to determine the relationship between the set \(\{T, M, C\}\) and the set \(\{T, M, C, R\}\). Specifically, we are asked to subtract the second set from the first set and determine whether the result is a subset of, equal to, both, or neither of the original sets.

Step 2 :The operation of subtracting one set from another involves removing all elements of the second set from the first set. In this case, all elements of the first set are also in the second set, so the result of the subtraction will be the empty set.

Step 3 :The empty set is a subset of all sets, including the original sets. Therefore, the \(\subseteq\) symbol can be placed in the blank to make the statement true.

Step 4 :The \(C\) symbol, which denotes set equality, cannot be placed in the blank because the empty set is not equal to either of the original sets.

Step 5 :Final Answer: Only \(\subseteq\) can be placed in the blank to make the statement true. Therefore, the correct answer is \(\boxed{\text{Only } \subseteq}\).

From Solvely APP
Source: https://solvelyapp.com/problems/18917/

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