Mathematics
Sid is given a few sets. These are represented as A, B, C, D, E, F and G on a plain sheet of paper as a Venn Diagram.
(1) How many empty sets are there in the given Venn Diagram ?
- 3
- 2
- 1
- 0
(2) How many singleton sets are there in the given Venn Diagram ?
- 0
- 1
- 2
- 3
(3) How many pairs of equivalent sets are there in the given Venn Diagram ?
- 1
- 2
- 3
- 4
(4) How many pairs of equal sets are there in the given Venn Diagram ?
- 0
- 1
- 2
- 3
Sets
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Answer
Sets in the diagram are:
A = {α, x, a, 1}
B = {1, 4}
C = {4}
D = {8, 7, 2, α, x}
E = {α, x, a, 1}
F = {7, 2, 4}
G = {8}
(1) An empty set has no elements.
Looking at the list above all sets A, B, C, D, E, F, and G contain at least one element. Therefore there are no empty sets.
Hence, option 4 is the correct option.
(2) A singleton set contains exactly one element.
C = {4}
G = {8}
Total singleton sets = 2
Hence, option 3 is the correct option.
(3) Equivalent sets have the same number of elements (n(A) = n(B)).
Pairs with same number of elements:
A and E (4 elements)
C and G (1 element)
Total pairs = 2
Hence, option 2 is the correct option.
(4) Equal sets must have the exact same elements.
Pairs with same elements:
A and E = {α, x, a, 1}
Hence, option 2 is the correct option.
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Related Questions
Fill in the blanks :
(i) In a …………… form, we list the properties satisfied by each element of the set.
(ii) A void set is usually denoted by …………… .
(iii) If A ⊆ X, then X is called a …………… of A.
(iv) Two finite sets having the same number of elements are said to be …………… .
(v) n(A ∪ B) + n(A ∩ B) = …………… .
Write true (T) or false (F):
(i) The number of proper subsets of a set containing n elements is 2n.
(ii) Any set A and its complement are equivalent sets.
(iii) The complement of a set is a subset of U.
(iv) If n(A ∩ B) = Φ, then n(B - A) = n(B)
(v) If two sets A and B are disjoint, then n(A ∪ B) = n(A) + n(B)
In a class there are 27 students. Out of these 14 study Psychology and 19 study Geography. There are 11 students who study both Psychology and Geography.
(1) How many students study Psychology but not Geography ?
- 3
- 4
- 5
- 6
(2) How many students study Geography but not Psychology ?
- 7
- 8
- 9
- 11
(3) How many students study neither Psychology nor Geography ?
- 8
- 7
- 6
- 5
(4) What is the difference between the number of students who study Psychology only and those who study Geography only ?
- 4
- 5
- 6
- 7
Assertion: The collection of all tall girls of your class is not a set.
Reason: A well defined collection of objects is called a set.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true but Reason (R) is false.
- Assertion (A) is false but Reason (R) is true.