Name all subsets for {2,8} and how do i solve this complex fraction?

Question

1) Name all subsets for {2,8}
2) Complex Fraction Problem: (x/y) - 1/ (x^2/y^2) -1 = ?????

Answer 1

{ } (the null set)
{2}
{8}
{2,8}

I'll let you work out the algebraic manipulation in the 2'nd one. You need the practice a --lot-- more than I do ☺

Doug

Answer 2

For subsets, always remember that a set is a subset of itself, and the empty set is always a subset also.

1) The subsets are {2,8} , {2} , {8} , { }

2) First simplify each fraction to get

x / y - y^2 / x^2 -1

then get a greatest common denominator, which is y*x^2

x^3 / y*x^2 - y^3 / y*x^2 - y*x^2 / y*x^2

then do your subtraction and get

(x^3 - y^3 - y*x^2) / (y*x^2)

It's possibly to write that differently if you factor the difference of cubes in the numerator, but there's nothing to cancel out from the top and bottom of the fraction.

Answer 3

The subsets of {2, 8} are
{2,8} *any set is a subset of itself
the empty set *the empty set is a subset of any set
{2}
{8}

Basically, if a set contains n elements, then it will have 2^n subsets. In your problem, the set has two elements, so it should have 2^2 = 4 subsets.