SET THEORY PRACTICE WORKSHEET FOR GRADE 11
About "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. Solution
(iii) {x ∈ N : 4x + 9 < 52}. Solution
(iv) {x : (x−4)/(x+2) = 3, x ∈ R − {−2}}. Solution
(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) Solution
(5) Justify the trueness of the statement:
“An element of a set can never be a subset of itself.”
(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
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
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
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
