Question

Let U be the universal set and AU BUC = U. Then {(A - B) U (B-C) U(C - A)}' is equal to
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Answer 1

Given,

A U B U C =u

using venn diagram we have,

(A-B)=A

(B-C)=B

(C-A)=C

therefore,

(A-B)U(B-C)U(C-A)=

(A U B U C)-(A n B n C)

{(A-B)U(B-C)U(C-A)}´=A n B n C

Answer 2

$\left \{ (A-B)\cup(B-C)\cup (C-A)\right \}'=A\cap B\cap C$

Step-by-step explanation:

Given:Universal set=U

Three set A, B and C

$A\cup B\cup C=U$

$A-B=A-A\cap B$

$B-C=B-B\cap C$

$A-C=A-A\cap C$

$\left \{(A-B)\cup(B-C)\cup (C-A)\right \}'=U-\left \{(A-B)\cup(B-C)\cup(C-A)\right \}$

We know that

$U-\left\{A-B)\cup(B-C)\cup(C-A)\right \}=A\cap B\cap C$

Therefore,

$\left \{ (A-B)\cup(B-C)\cup (C-A)\right \}'=A\cap B\cap C$

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