1.
{a, e, i, o}
{a} , {e} , {i} , {o} , {a,e} , {a,i} , {a,o} , {e,i} , {e,o} , {i,o} , {a,e,i} , {a,e,o} , {a,i,o}
2.
{0, 1, 2}
{0} , {1} , {2} , {0,1} , {0,2} , {1,2}
3.
Suppose U = {1, 2, 3, 4, 5} is the universal set and A = {2, 3}. What is A ?
Well "A" is {2, 3}, but I'm guessing you meant A'.
A' is all the numbers you don't see, which is
{1, 4, 5}
4.
Suppose U={1, 2, 3, 4, 5, 6, 7, 8} is the universal set and P={2,4, 6, 8}. What is P?
Again, "P" is just {2,4, 6, 8}, but P' is all the numbers you don't see, which are all prime numbers in this sequence:
{1, 3, 5, 7}
5.
-4 < k + 3 < 8
subtract 3 from all sides
-7 < k < 5
6.
5 <= y + 2 <= 11
subtract 2 from all sides
3 <= y <= 9
7.
6b - 1 < -7 or 2b + 1 > 5
solve both
6b - 1 < -7
add both sides by 1
6b < -6
divide both sides by 6
b < -1
now do the other problem
2b + 1 > 5
subtract both sides by 1
2b > 4
divide both sides by 2
b > 2
answer: b < -1 or b > 2
8.
5 + m > 4 or 7m < -35
subtract both sides by 5 |or| divide both sides by 7
m > -5 or m < -5
m = -5
