Confusion about notation regarding compliments/universal sets

Using the line is similar to using parentheses with statements.

For example, the meaning of " not in ( A or B)" is different than the meaning of "(not in A) or (not in B)"

Suppose a vase V is (not alabaster) and is blue.

Then it is is true that "(V is not alabaster) or (V is not blue)"
because V is not alabaster.

It is false that "V is not (alabaster or blue)"
because V is blue, hence it IS (alabaster or blue).

 

let us first understand the basic concepts involved-

A,B are the name of the sets involved

A U B refers to a collection that includes all elements that occur in A and (or) B i.e. those that occur in A only + those that occur in B only + those that occur in both of them

A bar over a set means that we've to take negation of that set.

[itex]\cap[/itex] symbol means intersection and considers only those elements that are common to both the sets

now, a bar over whole of ( A U B ) means that we have to take those elements in father or universal set defined for the two sets which don't occur in the set ( A U B )

and the part b refers to the elements which are common between ( the elements contained in father set but not in set A ) and ( the elements contained in father set but not in set B )