प्रश्नावली 1.5
प्रश्न 1.
U = {1, 2, 3, 4, 5, 6, 7, 8, 9), A = {1, 2, 3, 4),
B = (2, 4, 6, 8) 3. C = {3, 4, 5, 6}
तो निम्नलिखित को ज्ञात कीजिए:
(i) A'
(ii) B'
(iii) (A u C)'
(iv) (AUB)
(v) (A')'
(vi) (B – C)
हल:
(1) A' = U - A (1, 2, 3, 4, 5, 6, 7, 8, 9)-(1, 2, 3, 4) (5,6,7,8,9)
(B'= U-B=(1, 2, 3, 4, 5, 6, 7, 8, 9)-(2, 4, 6, 8) = (1,3,5,7,9)
=
() AuC (1, 2, 3, 4) u (3, 4, 5, 6) (1, 2, 3, 4, 5, 6) (AUC) U-(AUC) = {1, 2, 3, 4, 5, 6, 7, 8, 9){1, 2, 3, 4, 5, 6) = {7, 8, 9)
(iv) AuB (1, 2, 3, 4) u (2, 4, 6, 8) = {1, 2, 3, 4, 6, 8)
(Au B) U-(AUB) = {1, 2, 3, 4, 5, 6, 7, 8, 9)-(1, 2, 3, 4, 6, 8) = {5, 7, 9}
(v) (A)'= UA = {1, 2, 3, 4, 5, 6, 7, 8, 9) - {1, 2, 3, 4} = {5, 6, 7, 8, 9) (A')'=
U-A' = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {5, 6, 7, 8, 9} = {1, 2, 3, 4}
(vi B - C - {2, 4, 6, 8) - (3, 4, 5, 6) = {2, 8) (B - C) = U - (B - C) = {1, 2, 3, 4, 5, 6, 7, 8, 9) (28) (1,3,4,5,6,7,9)
प्रश्न 2.
यदि U = {a, b, c, d, e, f, g, h}, तो निम्नलिखित समुच्चयों के पूरक ज्ञात कीजिये:
(i) A = {a, b, c)
(i) B (d, e, f,g)
(iii) C = (a, c, e, g)
(iv) D (f, g, h, a)
हल:
(AU-A (a, b, c, d, e, f, g, h)-(a, b,c) (d, e, f, g, h)
=
(i) BUB(a, b, c, d, e, f, g, h)-(d, e, f, g) (a, b, c, h)
C U-C(a, b, c, d, e, f, g, h) (a, c, e, g) (b, d, f, h)
(iv) D'=U-D = (a, b, c, d, e, f, g, h)-(f, g, h, a) = (b, c, d, e).
