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The truth function

Let Sbe a compound statement. We can define a function

JS.

called the truth function of S, in the following way

1    IfS contains the n distinct statement variahles

p 1, p2,pn, and no others, then the truth function fSis a

function of n variables xl, x2.....xn, each ofwhich can

take on the values 1 or 0.

2    The value offS(x\, x2, xn) is defined to be truth value

of the statement S, when the simple statements

p 1, p2,pnare given the truth values x 1, x2, xn,

respectively.

Example Lel's 5 be a statement: (pA~ą) <==>{ ~]i ==>q). According to the truth table, the values of truth function are:

fS( 1, 1) = 0,/S(l, 0) = l,fS(0, 1) = 0,fS(0, 0) = 1.

Two compound statements are logicaliy equivalent if they

always have the same truth value. We denote this as A =B.