Let f, e, and c be propositions and s be a statement. f: "You have the flu." e: "You miss the final exam." c: "You pass the course." s: "A necessary conditions for you to pass the course are not to miss the final exam and not to have the flu." Which expression (A, B, C) express the given statement s using f, e, c, and logical connectives including negations. A: (~ eV ~ f → c) B: (~ e^ ~ f → c) C: (c en ~ f)
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.
Please follow bartleby guidelines and answer the two questions.
f: "You have the flu"
~f: "You do not have the flu"
e: "You miss the final exam"
~e: "You do not miss the final exam"
c: "You pass the course"
statement s: "A necessary conditions for you to pass the course are not to miss the final exam and not to have the flu."
The logical connectives including negations of s is (~e~fc).
Hence option B is correct.
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