Q1 of 43 Page 11

If A = {a, b, c, d, e}, B = {c, d, e, f}, C = {b, d} and D = {a, e}.

then which of the following statements are true and which are false?


i. C ⊆ B ii. A ⊆ D
iii. D ⊆ B iv. D ⊆ A


v. B ⊆ A vi. C ⊆ A

We consider the following Venn diagram to check whether the above statements are true or not.


Now, we have A = {a, b, c, d, e}, B = {c, d, e, f}, C = {b, d} and D = {a, e}.


So, it is clear from above that every element of set C and set D is also an element of set A.


∴ C ⊆ A and D ⊆ A


Hence, (iv), (vi) are true and (ii) is false.


Also, it is clear from above that every element of set B is not an element of set A.


∴ (v) is false.


Similarly, it is clear that every element of set C is not an element of set B.


∴ (i) is false.


Also, every element of set D is not an element of set B.


∴ (iii) is false.


More from this chapter

All 43 →
3

Which of the following are empty sets? Why?

i. A = {a |a is a natural number smaller than zero.}


ii. B = {x|x2 = 0}


iii. C = {x|5x – 2 = 0, x ∈ N}

 4

Write with reasons, which of the following sets are finite or infinite. We know that if a set is a null set or number of elements are limited and countable then it is called ‘Finite set’ and if number of elements in a set is unlimited and uncountable then the set is called ‘Infinite set’.

i. A = {x|x < 10, x is a natural number}


ii. B = {y |y< -1, is an integer}


iii. C = Set of students of class 9 from your school.


iv. Set of people from your village.


v. Set of apparatus in laboratory


vi. Set of whole numbers


vii. Set of rational number

 2

Take the set of natural numbers from 1 to 20 as universal set and show set X and Y using Venn diagram.

i. X = {x | x ∈ ℕ, and 7 < x < 15}


ii. Y = {y | y ∈ ℕ, y is prime number from 1 to 20}

 3

U = {1, 2, 3, 7, 8, 9, 10, 11, 12}

P = {1, 3, 7, 10}


then (i) show the sets U, P and P � by Venn diagram. (ii) Verify (P’)’ = P