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QuestionDetermine if the statement C⊂DC \subset D is true or false, given the sets A={1,3,5,7}A=\{1,3,5,7\}, B={5,6,7,8}B=\{5,6,7,8\}, C={5,8}C=\{5,8\}, D={2,5,8}D=\{2,5,8\}, and U={1,2,3,4,5,6,7,8}U=\{1,2,3,4,5,6,7,8\}. If false, explain why.

Studdy Solution

STEP 1

Assumptions1. The set A contains the elements {1,3,5,7} . The set B contains the elements {5,6,7,8}
3. The set C contains the elements {5,8}
4. The set D contains the elements {,5,8}
5. The universal set U contains the elements {1,,3,4,5,6,7,8}
6. The symbol ⊂ means "is a subset of". A set A is a subset of a set B if every element of A is also an element of B.

STEP 2

We need to determine whether the statement "C is a subset of D" is true or false. We can do this by comparing the elements of set C to the elements of set D.

STEP 3

Let's list the elements of set C.
C={5,8}C = \{5,8\}

STEP 4

Now, let's list the elements of set D.
={2,,8} = \{2,,8\}

STEP 5

We can see that every element of set C is also an element of set D. Therefore, C is a subset of D.
C⊂DC \subset DThe statement is true.

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