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Math Help - statement logic, truth sets

  1. #1
    Newbie
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    Jan 2009
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    Red face statement logic, truth sets

    Hi I'm new to this forum

    and I need help with these exercises I got from the revision sheet


    1) NEGATE the following statements:

    i:
    There are at least 3 of us, who (each) weigh at least 200lbs.

    partial ideas: statement A: at least 3 of us; statement B: (weigh) at least 200lbs
    Whole setntence: A^B



    ii: If I graduate I'll go to college or travel around the world.

    partial ideas: statement A: I graduate; statement B: I'll go to college, statement C: I'll travel
    Whole sentence: ? A->(BvC)
    ? or ? (A-->B)v(A-->C)

    iii: I will be lying in bed and resting, or working.

    partial ideas: statement A: I will be lying in bed; statement B: I will be resting; statement C: I will be working
    Whole sentence: (A^B)vC

    iv: A line is perpendicular to a plane if and only if it is perpendicular to all lines in that plane.

    partial ideas: statement A: a line is perpendicular to a plane; statement B: a line is perpendicular to all lines in that plane
    Whole setntence: A<-->B

    v: Everyone caught at least 10 fish (each).

    partial ideas: statement A: caught at least 10 fish
    Whole setntence: Vx :A

    vi: Everyone, in each fishing session, caught at least 10 fish (each in each session).

    NO IDEA



    vii: At least one of us (separately), caught at least 10 fish, in at least one fishing session (each).
    ((A possible situation that would satisfy the statement could be: 9 of us caught more than 12 fish each, each in 8 of 11 sessions. .We caught 9*12*8 fish + the ones where a single person
    caught less than 10 fish in one session, since we were, let's say, 13 people and had 11 sessions. ))

    partial ideas: at least one of us Ex;;; statement A: caught at least 10 fish;;; ? in at least one fishing session is statement B or Ey?

    viii: Vc > 0,Ed > 0, where |x-a|< d --> |f(x)-L|<c


    ix: Vx is an element of R Ey is an element of R, x+y=0


    V: universal quantifier E: existential quantifier



    2)
    Determine the domains for the statement forms

    i: A(x)vB(x) ii: A'(x) iii: B(x)-->A(x)

    where A(x): (x+3)/sqrt(x+3)=2; B(x): log(2-x)=1; C(x): (x/sqrt(2-log(x)))+((x+1)/(x-2004))=1

    well i don't really get this either but i guess
    normally following the algebra rules the domains for A,B,C if they're treated like functions would be A: ( -3; +infinity ); B: ( -infinity; 2 ); C: ( 0; 100 )

    3)
    Determine the truth sets for the statement forms i: A'(x)^C(x); ii: B(x)-->A(x)
    where A(x): x^2-9<0, B(x):3x+3(greater than/equal to)0, C(x):|2x-5|>4

    no idea what the truth sets are

    Thank you, I really appreciate your help
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  2. #2
    Junior Member
    Joined
    Jan 2009
    Posts
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    Post

    I'll help you with some of your questions:
    1)
    vi.

    Everyone, in each fishing session, caught at least 10 fish (each in each session).
    Let Fxz- x is in z fishing session.
    Gxy-x caught y fish.
    AxEyAz(Fxz->(Gxy&y>=10))
    Not sure if I got this right, though.

    3)
    Determine the truth sets for the statement forms i: A'(x)^C(x); ii: B(x)-->A(x)
    where A(x): x^2-9<0, B(x):3x+3(greater than/equal to)0, C(x):|2x-5|>4

    i) |2x-5|>4 means 2x-5>4 or 2x-5<-4 after rearranging this and combine it with the negation of A(x) which is x^2-9>=0 which means either x>=3 or x<=-3 you will get whatever answer it would be. for ii use material conditional where B(x)->A(x) is the same as: ~(B(x)&~A(x)).
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