Let A and B be sets such that AB. Consider the following statements: (1) If A is finite, then B is finite. (2) If A is infinite, then B is infinite. (3) If B is finite, then A is finite. (4) If B is infinite, then A is infinite. Which of the following is true? Statements (1) and (2) are true. Statements (1) and (3) are true. Statements (1) and (4) are true. Statements (2) and (3) are true. Statements (2) and (4) are true. Statements (3) and (4) are true. None of the above is correct.
To solve this problem, you need to understand the concept of sets and how they relate to each other. In particular, you need to know the definition of subset, which says that a set A is a subset of a set B, denoted A ⊆ B, if every element of A is also an element of B.
You also need to understand the concepts of finite and infinite sets. A set is considered finite if it has a certain number of elements, and infinite if it has an unlimited number of elements. For example, the set {1, 2, 3, 4} is finite, while the set of natural numbers {1, 2, 3, 4, ...} is infinite.
The problem gives four statements about the relationship between the sets A and B and whether they are finite or infinite. You must evaluate the truth value of each statement because A is a subset of B.
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