Advertisements
Advertisements
Question
If A and B are two set such that \[A \subset B\]then find:
\[A \cap B\]
Advertisements
Solution
From the Venn diagrams given below, we can clearly say that if A and B are two sets such that \[A \subset B\] then
Form the given Venn diagram, we can see that \[A \cap B\]= A
APPEARS IN
RELATED QUESTIONS
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 appropriate Venn diagram for the following:
A' ∩ B'
In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only.
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:
\[A \cup C\]
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\[B \cup D\]
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: \[A \cap D\]
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 \[A = \left\{ x: x \in N \right\}, B = \left\{ x: x - 2n, n \in N \right\}, C = \left\{ x: x = 2n - 1, n \in N \right\}\] and D = {x : x is a prime natural number}. Find: \[C \cap D\]
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that \[\left( A \cup B \right)' = A' \cap B'\]
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 .
Using the Venn diagram, examine the logical equivalence of the following statements:
(a) Some politicians are actors.
(b) There are politicians who are actors.
(c) There are politicians who are not actors.
From the given diagram find :
A ∪ B
From the given diagram find :
B - A
From the given diagram find :
(A ∪ B)'
Use the given Venn-diagram to find :
B'
Use the given Venn-diagram to find :
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 :
(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
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'
From the given diagram, find :
(i) (A ∪ B) - C
(ii) B - (A ∩ C)
(iii) (B ∩ C) ∪ A
Verify :
A - (B ∩ C) = (A - B) ∪ (A - C)
Using the given diagram, express the following sets in the terms of A and B. {a, d}
Using the given diagram, express the following sets in the terms of A and B. {a, d, c, f}
Using the given diagram, express the following sets in the terms of A and B. {a, d, g, h}
Using the given diagram, express the following sets in the terms of A and B. {g, h}
Represent the truth of the following statement by the Venn diagram.
Some hardworking students are obedient.
Represent the truth of the following statement by the Venn diagram.
If a quadrilateral is a rhombus, then it is a parallelogram.
Represent the following statement by the Venn diagram.
No circle is rectangle.
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.
Some of the students study Mathematics but do not study English, some study English but do not study Mathematics, and some study both.
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 students are not scholars
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}
