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The truth function

Let Sbe a compound statement. We can define a function

fs.

called the truth function ofS, in thefollowing way

1    IfS contains the n distinct statement vańables

pl, p2,..., pn, and no others, then the truth function fSis a

function ofn variablesx 1, x2,xn, each ofwhich can take on the values 1 or 0.

2    The value offS(xl, x2,xń) is defined to be truth value

of the statement S, when the simple statements

pl, p2,pnare given the truth values xl, x2,xn,

respectively.

Example Let’s S be a statement: (pA~q) <==>(~p ==>q).

According to the truth table, the values of truth function are:

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

Two compound statements are logically eąuiyalent if they

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