Let A and B be two sets such that : n(A) = 20, n(A∪B) = 42 and n(A⋂B) = 4. Find (i) n(B) (ii) n(A-B) (iii) n(B-A)

Find n(B), n(A−B) and n(B−A)

Question:

Let \( A \) and \( B \) be two sets such that:

\[ n(A)=20,\quad n(A\cup B)=42,\quad n(A\cap B)=4 \]

Find:

\[ (i)\ n(B) \] \[ (ii)\ n(A-B) \] \[ (iii)\ n(B-A) \]

Solution

(i) Find \( n(B) \)

\[ n(A\cup B)=n(A)+n(B)-n(A\cap B) \] \[ 42=20+n(B)-4 \] \[ 42=16+n(B) \] \[ n(B)=26 \]

(ii) Find \( n(A-B) \)

\[ n(A-B)=n(A)-n(A\cap B) \] \[ =20-4 \] \[ =16 \]

(iii) Find \( n(B-A) \)

\[ n(B-A)=n(B)-n(A\cap B) \] \[ =26-4 \] \[ =22 \]

Hence,

\[ \boxed{n(B)=26} \] \[ \boxed{n(A-B)=16} \] \[ \boxed{n(B-A)=22} \]

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