Decide whether the following statements asserting set relationships are true or false. (a) \( \{m, i, x, u, p\}=\{i, n, b, u, x\} \) (b) \( \{10\} \subset\{10,12,14\} \) (c) \( \{5,15,19\}=\{15,19,5\} \) (a) Choose the correct answer below. A. The statement is false. The sets do not contain the same elements. B. The statement is true. The sets contain the same elements. C. The statement is true. If at least one element is listed in both sets, then the two sets are equal. D. The statement is false. The two sets list the same elements, but order does matter. (b) Choose the correct answer below. A. The statement is true because \( A \subset B \) means that every element of \( A \) is also an element of \( B \). B. The statement is true because 10 is in \( \{10,12,14\} \) and both sets are not the same. C. The statement is false because if \( A \subset B \), but \( A \neq B, A \) is a proper subset of \( B \). D. The statement is false because \( A \subset B \), in this example, is the empty set. (c) Choose the correct answer below.

**(a) Analyzing \(\{m,i,x,u,p\} = \{i,n,b,u,x\}\):** - The first set is \(\{m,i,x,u,p\}\) which contains the elements \(m,\ i,\ x,\ u,\ p\). - The second set is \(\{i,n,b,u,x\}\) which contains the elements \(i,\ n,\ b,\ u,\ x\). - Comparing the two, the first set has \(m\) and \(p\) while the second set has \(n\) and \(b\). Since the elements are different, the two sets are not equal. **Answer for (a):** **A.** The statement is false. The sets do not contain the same elements. --- **(b) Analyzing \(\{10\} \subset \{10,12,14\}\):** - The set \(\{10\}\) contains only the element \(10\). - The set \(\{10,12,14\}\) contains \(10\), \(12\), and \(14\). - Since every element of \(\{10\}\) (in this case just \(10\)) is also an element of \(\{10,12,14\}\), the subset relationship holds. **Answer for (b):** **A.** The statement is true because \(\,A \subset B\,\) means that every element of \(A\) is also an element of \(B\). --- **(c) Analyzing \(\{5,15,19\} = \{15,19,5\}\):** - The first set is \(\{5,15,19\}\) and the second set is \(\{15,19,5\}\). - In set theory, the order of the elements does not affect equality. Both sets contain exactly the same elements: \(5\), \(15\), and \(19\). **Answer for (c):** The statement is true. The sets contain the same elements.