Expert: Sherry Wallin - 4/7/2010

Question
11. Let
A={x│x∈ N and 1<x<50}
B={x│x∈ R and 1<x<50}
C ={x│x∈ Z and |x|≥25}
Which of the following are true?
a. A ⊆ B
b. 17 ∈ A
e. √3 ∈ B
h. {x│x ∈ Z and x2 >625} ⊆ C

Answer
Hi Ashley~
    For part a you want to ask yourself if every element in the set A is also in the set B. The set A is the set of natural numbers, i.e., 2,3,...,49 excluding 1 and only going up through 49. The set B has all real numbers between 1 and 50 but not including 1 or 50. But keep in the mind that the real numbers are all the numbers you've ever used including irrationals and decimals etc. So it certainly has 2,3,...,49 in it so yes A is a subset of B. For part b, is 17 one of the natural (counting numbers) between 1 and 50? Well yes, so 17 is an element of A. For e, the square root of 3 is an irrational number which is in the set of real numbers and it is about 1.7 so it is certainly between 1 and 50. For h, I think you meant to say that x^2 > 625 and what they want you to do is tell what elements of h are in the set C. The square root of 625 is 25 so you want at least 26. Well since C is all integers whose absolute value is greater than 25 it ends up that any integer that has an absolute value greater than 25 will suffice. Look at it (h), h is just another way to say what C is:
{...,-27,-26,26,27,...}

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