elements of s

Question

Given a set S={x\ x is an even multiple of 3}.

a) Denote only four (4) elements of S.

b) Is S finite or infinite?
c) Which one of the following signs (ε and ε) should you use for: -9-----S

(the little Signs to Fill in are: “belong to” or “doesn’t belong to”!)

Answer 1

Rose,

 

Because it is an even multiple of 3, we can multiple this by 2 and then relate it to the +- integers as follows. Then the set members are functions of n and we don't have to worry about even or odd, just +- integers since you didn't state that x was positive.

 

S(x) = {x | where x = 6n  and n = 0, +-1, +-2, +-3, ... to +- infinity}

 

Note that x=zero is even because it is divisible by 2; but no odd number can be divisible by 2, and 0 clearly is, so zero can't be odd. However, some might keep it out of the set anyway, but I'll leave it in based on this argument.

 

(a) 4 elements of S(x) = {-6, 6, 12, 18}

(b) The set S(x) is infinite because n is infinite and so S can have an infinite number of elements.

(c) x = -9 is not an even multiple of 3 or a multiple of our 6 formulation so it is not in S(x).  I can't type the symbol here, but you would use the with a slash thru it to denote "not a member of the defined set".