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The truth function Let S be a compound statement. We can define a function f S , called the truth function of S , in the following way 1 If S contains the n distinct statement variables p 1 , p 2 , ..., p n , and no others, then the truth function f S is a function of n variables x 1 , x 2 , ..., x n , each of which can take on the values 1 or 0. 2 The value of f S ( x 1 , x 2 , ..., x n ) is defined to be truth value of the statement S , when the simple statements p 1 , p 2 , ..., p n are given the truth values x 1 , x 2 , ..., x n , respectively. Example Let's S be a statement: ( p ∧ ∼ q ) ⇐⇒ ( ∼ p = ⇒ q ) . According to the truth table, the values of truth function are: f S (1 , 1) = 0 , f S (1 , 0) = 1 , f S (0 , 1) = 0 , f S (0 , 0) = 1 . Two compound statements are logically equivalent if they always have the same truth value. We denote this as A ≡ B .
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