# SET THEORY PRACTICE WORKSHEET FOR GRADE 11

Set Theory Practice Worksheet For Grade 11 :

Here we are going to see some practice questions on set theory.

(1)  Write the following in roster form.

(i) {x ∈ N : x2 < 121 and x is a prime}.     Solution

(ii) the set of all positive roots of the equation (x − 1)(x + 1)(x2 − 1) = 0.

(iii)  {x ∈ N : 4x + 9 < 52}.

(iv)  {x : (x−4)/(x+2) = 3, x ∈ R − {−2}}.

(2)  Write the set {−1, 1} in set builder form.       Solution

(3)  State whether the following sets are finite or infinite.

(i) {x ∈ N : x is an even prime number}.      Solution

(ii) {x ∈ N : x is an odd prime number}.      Solution

(iii) {x ∈ Z : x is even and less than 10}.      Solution

(iv) {x ∈ R : x is a rational number}.      Solution

(v) {x ∈ N : x is a rational number}.      Solution

(4)  By taking suitable sets A,B,C, verify the following results:

(i) A × (B ∩ C) = (A × B) ∩ (A × C).      Solution

(ii) A × (B ∪ C) = (A × B) ∪ (A × C)         Solution

(iii) (A × B) ∩ (B × A) = (A ∩ B) × (B ∩ A)       Solution

(iv) C − (B − A) = (C ∩ A) ∪ (C ∩ B').       Solution

(v) (B − A) ∩ C = (B ∩ C) − A = B ∩ (C − A).       Solution

(vi) (B − A) ∪ C = (B ∪ C) − (A − C)

(5)  Justify the trueness of the statement:

“An element of a set can never be a subset of itself.”

Solution

(6)  If n(P(A)) = 1024, n(A ∪ B) = 15 and n(P(B)) = 32, then find n(A ∩ B).                Solution

(7)  If n(A ∩ B) = 3 and n(A ∪ B) = 10, then find n(P(AΔB)).             Solution

(8)  For a set A, A × A contains 16 elements and two of its elements are (1, 3) and (0, 2). Find the elements of A.

(9)  Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y, z are distinct elements.             Solution

(10)  If A × A has 16 elements, S = {(a, b) ∈ A × A : a < b} ; (−1, 2) and (0, 1) are two elements of S, then find the remaining elements of S.             Solution After having gone through the stuff given above, we hope that the students would have understood, "Set Theory Practice Worksheet For Grade 11"

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WORD PROBLEMS

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Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

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Remainder when 17 power 23 is divided by 16

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