Truth Tables

Truth Tables

Compound statements can be complicated and Truth Tables let you calculate with them.

An example

Professor says: If you get an A on the final, or you get at least 90 on the homework, then you pass this course.

This statement is TRUE provided that the Professor told the truth (didn’t lie) – whether or not you get an A in the course.

Analysis

  • You get an A in this course (P)
  • You get an A on the final (Q)
  • You get at least 90 on the homework (R)

The promise is:

If (Q or R) then P.

How many possibilities?

Truth Table

\[(Q\vee R)\implies P\]

Another example (see the text, Ch2.5)

Let \(P\) and \(Q\) be any statements. \((P\vee Q)\wedge\sim(P\wedge Q)\) reads as:

(\(P\) OR \(Q\)) and NOT (\(P\) AND \(Q\)).

Example

\(P\iff(Q\vee R)\)

  • \(xy=0\) if and only if \(x=0\) or \(y=0\).
  • You will pass this course if and only if you get an \(A\) on the final or at least 90 on the homework.

Homework example

Write a truth table for \((P\wedge \sim P)\vee Q\).