Results 1 to 3 of 3

Math Help - help me

  1. #1
    Member
    Joined
    Jul 2006
    Posts
    95

    help me

    please help me to slove that.
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Question 1 is wrong, unless :r means not r.

    If r is true (the way I see it) then p, q being false still keep the statement true.

    If r is false (which I am assuming) then both p,q cannot be false because that would imply p v (q v r)=FALSE
    Thus, one of p,q is true
    Thus, p v q=TRUE
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,676
    Thanks
    608
    Hello, m777!

    I assume you are familiar with these definitions, properties and axioms.

    p → q . . ~p V q . . . . . . . .Definition of Implication

    p V q . . q V p . . . . . . . . . Commutative property of Disjunction

    p V (q V r) . . (p V q) V r . . Associative property of Disjunction

    p V ~p . . t . . . . . . . . . . . Axiom #1

    t V p . . t . . . . . . . . . . . . .Axiom #2


    3(b) Deterine whether the statement is a tautology, a contingency, or absurdity.

    . . p → (q → p)


    We have: .p → (q → p)

    . . . . . . . .p → (~q V p) . . . .Def. of Implication

    . . . . . . . ~p V (~q V p) . . . Def. of Implication

    . . . . . . . (~p V p) V ~q . . . Comm/Assoc properties

    . . . . . . . . . . t V ~q . . . . . .Axiom #1

    . . . . . . . . . . . .t . . . . . . . . Axiom #2


    The statement is always true . . . It is a tautology.



    (A truth table would have been faster . . . )
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum