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Exercise 1.3
1. Make correct statements by filling in the symbols or
in the blank spaces:
(i) {2, 3, 4} _______ {1, 2, 3, 4, 5}
(ii)
(iii) { is a student of class XI of your school} _______ {
student of your school}
(iv) { is a circle in the plane} _______ {
is a circle in the same plane with 1 unit}
(v) { is a triangle in plane} _______ {
is a rectangle in the same plane}
(vi) { is an equilateral triangle in a plane} _______ {
is a rectangle in the same plane}
(vii) { is an even natural number} _______ {
is an integer}
Ans. (i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
2. Examine whether the following statements are true or false:
(i)
(ii) {
is a vowel in the English alphabet}
(iii)
(iv)
(v)
(vi) { is an even natural number less than 6}
{
is a natural number which divide 36}
Ans. (i) Let A = and B =
Here, every element of set A is an element of set B.
A
B
Therefore, statement is false.
(ii) Let A = and B
= { is a vowel in the English alphabet}
=
Here, every element of set A is an element of set B.
A
B
Therefore, statement is true.
(iii) Let A = {1, 2, 3} and B = {1, 3, 5}
Here, 2 A but 2
B
A
B
Therefore, statement is false.
(iv) Let A = and B =
Here, every element of set A is an element of set B.
A
B
Therefore, statement is true.
(v) Let A = and B =
Here, B
Therefore, statement is false.
(vi) Let A = { is an even natural number less than 6}
= {2, 4}
And B = }{
is a natural number which divide 36}
= {1, 2, 3, 4, 6, 12, 18, 36]
Here, every element of set A is an element of set B.
A
B
Therefore, statement is true.
3. Let A = {1, 2, {3, 4}, 5}. Which of the following statements are incorrect and why:
(i) {3, 4} A
(ii) {3, 4} A
(iii) {{3, 4}} A
(iv) 1 A
(v) 1 A
(vi) {1, 2, 5} A
(vii) {1, 2, 5} A
(viii) {1, 2, 3} A
(ix) A
(x) A
Ans. (i) {3, 4} is a member of set A.
{3, 4}
A
Therefore, {3, 4} A is incorrect.
(ii) {3, 4} is a member of set A. Therefore, {3, 4} A is incorrect.
(iii) {3, 4} is a member of set A.
{{3, 4}} is a set.
Therefore, {{3, 4}} A is incorrect
(iv) 1 is a member of set A. Therefore 1 A is correct.
(v) 1 is not a set, it is a member of set A. Therefore, 1 A is incorrect.
(vi) 1, 2, 5 are the members of set A.
{1, 2, 5} is a subset of set A.
Therefore, {1, 2, 5} A is correct.
(vii) 1, 2, 5 are the members of set A.
{1, 2, 5} is a subset of set A.
Therefore, {1, 2, 5} A is incorrect.
(viii) 3 is not a member of set A.
{1, 2, 3} is not a subset of set A.
Therefore, {1, 2, 3} A is incorrect.
(ix) is not a member of set A. Therefore,
A is correct.
(x) is not a member of set A. Therefore,
A is incorrect.
4. Write down all the subsets of the following sets:
(i)
(ii)
(iii) {1, 2, 3}
(iv)
Ans. (i) Number of elements in given set = 1.
Number of subsets of given set = = 2
Therefore, Subsets of given set are
(ii) Number of elements in given set = 2
Number of subsets of given set = = 4
Therefore, Subsets of given set are
(iii) Number of elements in given set = 3
Number of subsets of given set = = 8
Therefore, Subsets of given set are
(iv) Number of elements in given set = 0
Number of subsets of given set = = 1
Therefore, Subsets of given set are
5. How many elements has P(A), if A = ?
Ans. Number of elements in set A = 0
Number of subsets of given set = = 1
Therefore, number of elements of P (A) is 1.
6. Write the following as intervals:
(i) { R,
}
(ii) { R,
}
(iii) { R,
}
(iv) { R,
}
Ans. (i) Let A = { R,
}
It can be written in the form of interval as
(ii) Let A = { R,
}
It can be written in the form of interval as
(iii) Let A = { R,
}
It can be written in the form of interval as
(iv) Let A = { R,
}
It can be written in the form of interval as
7. Write the following intervals in set-builder form:
(i)
(ii) [6, 12]
(iii) (6, 12]
(iv)
Ans. (i) { R,
}
(ii) { R,
}
(iii) { R,
}
(iv) { R,
}
8. What universal set(s) would you propose for each of the following:
(i) The set of right triangles
(ii) The set of isosceles triangles
Ans. (i) Right triangle is a type of triangle. Therefore, the set of triangles contain all types of triangles.
U = {
is a triangle in plane}
(ii) Isosceles triangle is a type of triangle. Therefore, the set of triangles contain all types of triangles.
U = {
is a triangle in plane}
9. Given the set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, which of the following may be considered as universal set(s) for all the three sets A, B and C:
(i) {0, 1, 2, 3, 4, 5, 6}
(ii)
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
(iv) {1, 2, 3, 4, 5, 6, 7, 8}
Ans. (i) {0, 1, 2, 3, 4, 5, 6} is not a universal set for A, B, C because 8 C but 8 is not a member of {0, 1, 2, 3, 4, 5, 6}.
(ii) is a set which contains no element. therefore, it is not a universal set for A, B, C.
(iii) {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set for A, B, C because all members of A, B, C are present in {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
(iv) {1, 2, 3, 4, 5, 6, 7, 8} is not a universal set for A, B, C because 0 C but 0 is not a member of {1, 2, 3, 4, 5, 6, 7, 8}.
Ap apna first sum ka 4th part dekho galat hai??
Q2 no.6 Does 4 divide 36 ? I don’t think it does. So the answer will be false.
Sorry. The answer is correct.
?????
Nicely way to help student thank you so much