Conjunctions and disjunctions

Conjunctions and disjunctions

Lessons

Notes:

A conjunction is a compound statement that is made by combining two or more statements with the word "and". If any of the statements is false, then the entire conjunction is false. If all statements are true, then the conjunction is true. We can replace the word "and" with the symbol ˄.

A disjunction is a compound statement that is made by combining two or more statements with the word "or". If any of the statements is true, then the entire disjunction is true. If all statements are false, then the disjunction is false. We can replace the word "or" with the symbol ˅.

  • Introduction
    Conjunctions and Disjunctions Overview:
    a)
    Conjunctions

    b)
    Disjunctions


  • 1.
    Conjunctions

    Determine the truth value of the following conjunctions:

    a)
    A square is a 4-sided polygon and a rectangle is a 5-sided polygon

    b)
    10+7×2=72 10+7\times 2=72 and 10×7+2=7210\times 7+2=72

    c)
    March is the third month of the year and December is the last month of the year


  • 2.
    The symbols represent the following statements:

    pp: A year has 52 weeks
    qq: December is a summer month
    rr: A kilogram is 1000 grams

    Find the truth value of the following:
    a)
    pp ˄ qq

    b)
    pp ˄ rr

    c)
    pp ˄ ~qq

    d)
    ~rr ˄ ~pp

    e)
    pp ˄ ~qq ˄ rr

    f)
    ~pp ˄ qq ˄ ~rr


  • 3.
    Disjunctions

    Determine the truth value of the following disjunctions:

    a)
    1 metre is 100 centimetres or 1 metre is 10 centimetres.

    b)
    A right triangle always has an angle that is 90° degrees or the angles of a square are always 90° degrees.

    c)
    Breakfast is a meal or all meals are breakfasts.


  • 4.
    The symbols represent the following statements:

    pp: A week has 5 days
    qq: A day has 24 hours
    rr: An hour has 60 seconds

    Find the truth value of the following:
    a)
    pp ˅ qq

    b)
    pp ˅ rr

    c)
    pp ˅ ~qq

    d)
    ~rr ˅ ~pp

    e)
    ~pp ˅ qq ˅ ~rr

    f)
    pp ˅ ~qq ˅ ~rr


  • 5.
    Advanced Questions on Conjunctions and Disjunctions

    Let pp and qq be statement. Fill in the blanks:

    a)
    If pp is false, then pp ˄ qq is _______________.

    b)
    If pp is true, then pp ˅ qq is _______________.

    c)
    If ~pp is true, then pp ˄ qq is _______________.