Questions: Tell whether the statement below is true or false. U is the universal set. Let U=t, u, v, w, x, y, z, A=y, w, B=z, t, v, x, w, C=x, v, t, and D=w, v. There are exactly 9 subsets of C. Choose the correct answer below. False True

Tell whether the statement below is true or false. U is the universal set. Let U=t, u, v, w, x, y, z, A=y, w, B=z, t, v, x, w, C=x, v, t, and D=w, v.
There are exactly 9 subsets of C.

Choose the correct answer below.
False
True

Transcript text: Tell whether the statement below is true or false. $U$ is the universal set. Let $U=\{t, u, v, w, x, y, z\}, A=\{y, w\}, B=\{z, t, v, x, w\}, C=\{x, v, t\}$, and $D=\{w, v\}$. There are exactly 9 subsets of $C$. Choose the correct answer below. False True

Solution

Solution Steps

Step 1: Identify the set \( C \)

The set \( C \) is given as \( C = \{x, v, t\} \).

Step 2: Determine the number of elements in \( C \)

The set \( C \) has 3 elements: \( x \), \( v \), and \( t \).

Step 3: Calculate the number of subsets of \( C \)

The number of subsets of a set with \( n \) elements is \( 2^n \). Since \( C \) has 3 elements, the number of subsets is \( 2^3 = 8 \).

Step 4: Compare the calculated number of subsets with the given statement

The statement claims that there are exactly 9 subsets of \( C \). However, based on the calculation, there are only 8 subsets.

Step 5: Conclude whether the statement is true or false

Since the number of subsets of \( C \) is 8, not 9, the statement is False.

Final Answer

The correct answer is False.

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