Truth tables

Truth tables

Lessons

Notes:

We can organize truth values of statements by using a truth table.
  • Introduction
    Truth Tables Overview:
    a)
    Negation Truth Tables

    b)
    Conjunction Truth Tables

    c)
    Disjunction Truth Tables

    d)
    Truth Tables with three or more statements


  • 1.
    Truth Tables with Negations, Conjunctions, and Disjunctions (two statements)

    Fill in the truth tables:

    a)
    pp qq ~pp ~pp ˅ qq
    T T
    T F
    F T
    F F

    b)
    pp qq ~qq pp ˄ ~qq
    T T
    T F
    F T
    F F

    c)
    pp qq ~pp ~qq ~pp ˄ ~qq
    T T
    T F
    F T
    F F


  • 2.
    Construct a truth table for the following:
    a)
    pp ˅ ~qq

    b)
    ~pp ˄ qq


  • 3.
    Truth Tables with Negations, Conjunctions, and Disjunctions (three statements)

    Fill in the truth tables:

    a)
    pp qq rr ~pp ~pp ˅ qq (~pp ˅ qq) ˄ rr
    T T T
    T T F
    T F T
    F T T
    T F F
    F F T
    F T F
    F F F

    b)
    pp qq rr ~pp ~qq ~pp ˄ ~qq (~pp ˄ ~qq) ˅ rr
    T T T
    T T F
    T F T
    F T T
    T F F
    F F T
    F T F
    F F F

    c)
    pp qq rr ~pp ~rr ~pp ˅ ~rr (~pp ˅ ~rr) ˄ qq
    T T T
    T T F
    T F T
    F T T
    T F F
    F F T
    F T F
    F F F


  • 4.
    Construct a truth table for the following:
    a)
    pp ˅ qq ˅ rr

    b)
    pp ˄ qq ˄ rr