Question

Suppose U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } is the universal set and Q = { 3, 6, 9 }. What is Q?

A- { 3, 6, 9 }
B- { 4, 5, 7, 8 }
C- { 1, 2, 4, 5, 7, 8, 10 }
D- { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

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For questions 4 and 5, suppose U = { 1, 2, 3, 4, 5, 6, 7, 8 }, A = { 1, 3, 5, 7 }, and B = { 4, 5, 6 }. Tell whether each statement is true or false.

4. A ⊆ B

5. B ⊆ U

Answer 1

The set Q is accurately represented by option A- { 3, 6, 9 }. The statement A ⊆ B is false because not all elements of A are in B, while B ⊆ U is true since all elements of B are within the universal set U.

Step-by-step explanation:

In the given universal set U = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }, the subset Q = { 3, 6, 9 } is presented. The correct answer to what is Q is option A- { 3, 6, 9 }, as it matches the given set exactly.

For the questions regarding set theory relations, let's consider the information provided for sets A and B:

A = { 1, 3, 5, 7 }

B = { 4, 5, 6 }

The statement A ⊆ B means A is a subset of B. This statement is false, as A has elements that are not in B. The elements 1, 3, and 7 are in A but not in B.

Looking at the relationship between set B and the universal set U, B ⊆ U is true because all elements of B are indeed in the universal set U.

Answer 2

1. A

2. A

3. C

4. False

5. True