Question

For any two sets A and B, prove that
(1) (AUB) - B = A-B
(ii) A-(
AB) = A-B
(iii) A-(A-B) = AB
(iv) A (B-A) = A UB INCERT EXEMPLAR)
(W) (A-B) U(ANB) = A
INCERT EXEMPLAR)
HINTS TO SELECTED PROBLEMS
We know that X - Y =XY'. So A' - B' = A' n (B) = A' B=Bn A' =B-A
1) A -(A - B) = A -(A B')= A (A B')' = A (A' U (B')') = A (A' B) = A B
etxeC-B. Then,
XEC - B xeC and x&B xEC and x&A → XEC - A
IAC
C-BCC-A.
ME IMPORTANT RESULTS ON NUMBER OF ELEMENTS IN SETS
nd Care finite sets, and U be the finite universal set, then
n(AUB) = n(A) + n(B) - n(
AB)
n(
AB) = n(A) + n(B) – A, B are disjoint non-void sets.
n(A - B) = n(A) - n(
AB) i.e.n(A - B) + n(
AB) = n(A)
1(A AB) = No. of elements which belong to exactly one of A or B
n((A - B) U (B - A))
= n(A - B) + n(B - A)
[: (A - B) and (B - A) are
n(A) - n(An B) + n (B) - n(
AB)
- n(A) + n(B) - 2 n(
AB)
Al + n(B) + n(C) - n(
AB) - n(
BC) - n(ANC) + n(​

Answer 1

Answer:

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Step-by-step explanation:

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