Q3 of 43 Page 11

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

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

P = {1, 3, 7, 10}


P’ = {x | x ∈ U and x ∉ P} = {2, 8, 9, 11, 12}


(i) The Venn diagram showing U, P and P’ is:



(ii) Now, we consider (P’)’


(P’)’ = {x | x ∈ U and x ∉ P’}


= {1, 3, 7, 10}


= P


Hence, (P’)’ = P.


More from this chapter

All 43 →
1

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

 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}

 4

A = {1, 3, 2, 7} then write any three subsets of A.

 5

(i) Write the subset relation between the sets.

P is the set of all residents in Pune.


M is the set of all residents in Madhya Pradesh.


I is the set of all residents in Indore.


B is the set of all residents in India.


H is the set of all residents in Maharashtra.


(ii) Which set can be the universal set for above sets?