Suppose P(z, v) is some binary predicate defined on a very small domain of discourse: just the integers 1. 2, 3, and 4. For each of the 16 pairs of these numbers, P(z,v) is either true or false, according to d lillnwing table (r values are rows, y values are columns). 1 2 3 4 1 T F F F 2FTT F 3 ттTT 4 FFFF For example. P(1, 3) is false, as indicated by the F in the first row, third column. Use the table to decide whether the following statements are true or false. 1. VriyP(z, y). • 2. EWa P(z,s). • 3. avyP(z, 9). * 4. VyirP(z,).
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.
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