Let A = {x belongs to Z absolute value -1 less than or equal to x less than or equal to 2}, B={2x - 3 absolute value x element of A} C={x element of R absolute value x = a over b, a element A, b element of B}
lets work through these. remember the notations used, what they mean and how sets are definedok, so
once you are able to interpret what the symbols mean, it is not so hard, right? now, lets write out the set
and
that means we evaluate the expression 2x - 3 for all the elements of A
so, not to confuse you, but say
then,
so,
now, finally,
so, you take each element of A and divide it by all the elements of B, one by one until you exhaust the elements of A. thus,
and you can write those in order if you like
Now, can you do the questions? i will remind you of the definitions
Let and be sets. Then,list the elements of (A union B) X B
list the elements of B\C
list the elements of A and the symmetric difference of C
(symmetric difference)
yes
nope(A U B) X B = {(-5,-1), (-3,0), (-1,1), (1,2)}
the first elements in the pairs should be the elements of the first set in the product, while the elements of the second set are the second elements in the pair.
example: X = {1,2,3} and Y = {a,b,c}
then X x Y = {(1,a), (1,b), (1,3), (2,a), (2,b), (2,c), (3,a), (3,b), (3,c)}
no, B\C is a set, not an ordered pair. it is the set containing all elements of B that are not in C. so you take the set B and if there are any elements in there that are also in C, you throw them out.B\C = (0,2)
nope. try this one again, using the new insight you gained from the last twoA sym. dif C = {1/5, 1/3, -1/5, 1/3, 2/5, 2/3, -2}
Is this anywhere close to right?
you may want to take a look here. they have definitions and examples. Note that "\" is the sybol for set difference. so A\B is the same as A - B. different notations for the same thing