Advertisements
Advertisements
प्रश्न
Use the given diagram to find:
(i) A ∪ (B ∩ C)
(ii) B - (A - C)
(iii) A - B
(iv) A ∩ B'
Is A ∩ B' = A - B?
Advertisements
उत्तर
(i) B ∩ C = {d, e, f, g, h,j} ∩ {h, i, j, k, l}
= {h, j}
∴ A ∪ (B ∩ C) = {a, b, c, d, g, h, i} ∪ {h, j}
= {a, b, c, d, g, h, i, j}
(ii) A - C = {a, b, c, d, g, h, i} - {h, i, j, k, l}
= {a, b, c, d, g}
∴ B - (A - C) = {d, e, f, g, h, j} - {a, b, c, d, g}
= {e, f, h, j}
(iii) A - B = {a, b, c, d, g, h, i} - {d, e, f, g, h, j}
⇒ A - B = {a, b, c, i} ...(I)
(iv) B' = {a, b, c ,i, k, l, m, n, p}
A ∩ B' = {a, b, c, d, g, h, i} ∩ {a, b, c, i, k, l, m, n, p}
⇒ A ∩ B' = {a, b, c, i} ...(II)
From I and II we can conclude A ∩ B' = A - B
APPEARS IN
संबंधित प्रश्न
Draw appropriate Venn diagram for the following:
A' ∪ B'
Draw a Venn diagram for the truth of the following statement :
All rational number are real numbers.
Express the truth of each of the following statements by Venn diagram :
(a) Some hardworking students are obedient.
(b) No circles are polygons.
(c) All teachers are scholars and scholars are teachers.
From the given diagram find :
A - B
Use the given Venn-diagram to find:
B - A
Draw a Venn-diagram to show the relationship between two overlapping sets A and B. Now shade the region representing :
A ∪ B
Draw a Venn-diagram to show the relationship between two sets A and B; such that A ⊆ B, Now shade the region representing :
A ∩ B
Two sets A and B are such that A ∩ B = Φ. Draw a venn-diagram to show the relationship between A and B. Shade the region representing :
B - A
Express the truth of the following statement by the Venn diagram.
No child is an adult.
Let U be the set of all boys and girls in a school, G be the set of all girls in the school, B be the set of all boys in the school, and S be the set of all students in the school who take swimming. Some, but not all, students in the school take swimming. Draw a Venn diagram showing one of the possible interrelationship among sets U, G, B and S.
