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
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.
Draw a Venn diagram for the truth of the following statement :
All rational number are real numbers.
If A and B are two set such that \[A \subset B\]then find:
\[A \cap B\]
Represent the union of two sets by Venn diagram for the following.
Y = {y | y is an odd number between 90 and 100}
Express the truth of the following statements with the help of Venn diagram:
(a) No circles are polygon
(b) If a quadrilateral is rhombus , then it is a parallelogram .
Use the given Venn-diagram to find :
A ∪ B
Using the given diagram, express the following sets in the terms of A and B. {a, d, c, f, g, h}
Draw the Venn diagrams to illustrate the following relationship among sets E, M and U, where E is the set of students studying English in a school, M is the set of students studying Mathematics in the same school, U is the set of all students in that school.
Not all students study Mathematics, but every students studying English studies Mathematics.
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.
Take the set of natural numbers from 1 to 20 as universal set and show set X using Venn diagram.
X = {x | x ∈ N, and 7 < x < 15}
