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).
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
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 )
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