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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.
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उत्तर
(a) Some hardworking students are obedient.
Let H: set of hardworking students
O: Set of obedient students
U: Set of all students
from Venn diagram the truth value is H ∩ O
(b) No circles are polygons.
Let C: Set of all circles
P: Set of all polygons
U:set of all closed figures
From Venn diagram the truth value is
C ∩ P= Φ
(c) All teachers are scholars and scholars are teachers.
Let T: Set of all teachers
S: Set of all scholars
U: Set of all human beings
From Venn diagram the truth value is T=S
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संबंधित प्रश्न
Draw appropriate Venn diagram for the following:
A' ∪ B'
Draw Venn diagram for the truth of the following statements :
Some rectangles are squares.
If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11} and D = {10, 11, 12, 13, 14}, find:
\[B \cup C\]
Let \[A = \left\{ x: x \in N \right\}, B = \left\{ x: x - 2n, n \in N \right\}, C = \left\{ x: x = 2n - 1, n \in N \right\}\] and D = {x : x is a prime natural number}. Find: \[B \cap D\]
Let A = {3, 6, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16} and D = {5, 10, 15, 20}. Find:
\[B - A\]
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that \[\left( A \cup B \right)' = A' \cap B'\]
U = {1, 2, 3, 7, 8, 9, 10, 11, 12}
P = {1, 3, 7, 10} then
- show the sets U, P and P' by the Venn diagram.
- Verify (P')' = P
Express the truth of each of the following statements using Venn diagrams:
(a) No circles are polygons
(b) Some quadratic equations have equal roots
From the given diagram find :
A' ∩ B
From the given diagram find :
(A ∪ B)'
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?
Using the given diagram, express the following sets in the terms of A and B. {a, d, c, f, g, h}
Represent the truth of the following statement by the Venn diagram.
All teachers are scholars and scholars are teachers.
Represent the following statement by the Venn diagram.
Some non-resident Indians are not rich.
Express the truth of the following statement by the Venn diagram.
Some persons are not politician.
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.
All the students who study Mathematics study English, but some students who study English do not study Mathematics.
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.
There is no student who studies both Mathematics and English.
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.
Draw Venn diagram for the following:
Some doctors are rich
Draw Venn diagram for the following:
Some students are not scholars
