Thread: 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

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)).