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How do you show that if B is included in C, then the power set of B is included in the power set of C?
Power set inclusion is a mathematical concept that refers to the relationship between two sets, where one set is a subset of the other. This means that every element in the first set is also an element in the second set, but the second set may contain additional elements.
Power set inclusion is typically denoted using the symbol "⊆" (subset) or "⊂" (proper subset). For example, if A and B are sets and A is a subset of B, it would be written as A ⊆ B. If A is a proper subset of B, it would be written as A ⊂ B.
When B is included in C, it means that every element in B is also an element in C. In other words, B is a subset of C. This can also be written as B ⊆ C.
In order to prove power set inclusion when B is included in C, you need to show that every element in B is also an element in C. This can be done by taking an arbitrary element from B and showing that it is also an element in C, using a proof by contradiction, or by using a Venn diagram to visualize the relationship between the two sets.
No, power set inclusion can only be proved when B is a subset of C. If B is not a subset of C, then it cannot be proven that every element in B is also an element in C. In fact, if B is not a subset of C, then it is possible for B and C to have no elements in common at all.