Example 2. Consider the proposition, if n>2, then n">4. Let n= 3, 1,3. It is always true when i∈R. Remark 1. We have TT, FF, FT, which all sounds reasonable. However, when premise is true consequence is false. It means we can reach wrong result from right basis step by step without fault It is ridiculous in our life To impress the understanding, consider the following examples Example 3. With the following assumption 1. If man can fly like a bird! 2. Everything in a folk world We can make many irrational assertion We hope they could help you. If you have any good examples, please sent me an ema 4 Connectives From the point of view of function, every connective can be taken as a function with form f {0,1}→{0,1 Definition 4(Truth function). An n-ary connective is truth functional if the truth value for a(Al ly determined by the truth value of Al Definition 5. A k-place Boolean function is a function from F, r to T, F]. We let F and T themselves to be 0-place Boolean functions Example 4. We can define as a Boolean function in Figure 4 f→(T,T T F F f→(T,F)=F F T T f→(F,T)=T FFTf→(F,F)=T Figure 4: Boolean function Let Ii(1, 2, .., In)=i, which is a projection function of i-th parameter. We have the following properties on truth function 1. For each n, there are 2- n-place Boolean functions. It can be easily calculated only if you just think about the truth table 0-ary connectives: T and F 3. Unary connectives: - ,I, T and F.Example 2. Consider the proposition, if n > 2, then n 2 > 4. Let n = 3, 1, −3. It is always true when n ∈ R. Remark 1. We have T T, F F, F T, which all sounds reasonable. However, when premise is true consequence is false. It means we can reach wrong result from right basis step by step without fault. It is ridiculous in our life. To impress the understanding, consider the following examples: Example 3. With the following assumption: 1. If man can fly like a bird! 2. Everything in a folk world. We can make many irrational assertion. We hope they could help you. If you have any good examples, please sent me an email. 4 Connectives From the point of view of function, every connective can be taken as a function with form f : {0, 1} k → {0, 1}. Definition 4 (Truth function). An n-ary connective is truth functional if the truth value for σ(A1, . . . , An) is uniquely determined by the truth value of A1, . . . , An. Definition 5. A k-place Boolean function is a function from {F, T} k to {T, F}. We let F and T themselves to be 0-place Boolean functions. Example 4. We can define → as a Boolean function in Figure 4. x1 x2 x1 → x2 f→(x1, x2) T T T f→(T, T) = T T F F f→(T, F) = F F T T f→(F, T) = T F F T f→(F, F) = T Figure 4: Boolean Function Let Ii(x1, x2, . . . , xn) = xi , which is a projection function of i-th parameter. We have the following properties on truth function. 1. For each n, there are 22 n n-place Boolean functions. It can be easily calculated only if you just think about the truth table. 2. 0-ary connectives: T and F. 3. Unary connectives: ¬, I , T and F. 4