Show that the following statement is false. If A and B are two sets of positive integers, then (A∪B)^'=A'∪B'. Include the following in your answer: What technique seems appropriate in this situation? Why? Prove this statement true. Explain the elements of all sets that you use in your answer.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Show that the following statement is false. If A and B are two sets of positive integers, then (A∪B)^'=A'∪B'. Include the following in your answer: What technique seems appropriate in this situation? Why? Prove this statement true. Explain the elements of all sets that you use in your answer.
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