Question 1193411
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The difference A-B, of two sets A and B is defined to be the set of all
elements in A that are ot in B. Use the Venn diagram to illustrate the
following sets:
(a) A − B ; (b) (A − B) ∩ (B − A) ; (c) (A ∪ B) − (A ∩ B) (d) U − A where
U denote the universal set.
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            I will give wording description for each case.


            I prefer wording descriptions,  because only with wording description real understanding comes.



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(a)  A - B  is the set of all elements from A that do not belong to B. 

     So,   A - B = A - (A ∩ B) :    A - B  is  what remains from A when (A ∩ B) is subtracted from A.    <U>ANSWER</U>



(b)  (A − B) ∩ (B − A).

      A - B  is the set of elements of A that do not belong to (A ∩ B).

      B - A  is the set of elements of B that do not belong to (A ∩ B).


      Therefore,  (A − B) ∩ (B − A)  is the empty set.



(c)  (A ∪ B) − (A ∩ B)  is the set of elements from the union of A and B, that do not belong to the intersection  (A ∩ B).

     In other words,  (A ∪ B) − (A ∩ B)  is the set of elements, that belong A_only  and B_only:

     we take the union of A and B and subtract the intersection (A ∩ B) from this union.



(d)  U - A  is the set of all elements of the universal set that do not belong to A.

     The set  (U - A)  is called the complement set to A.
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Solved : &nbsp;&nbsp;&nbsp;&nbsp;I completed my description.


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