Set Theory and types of Sets MCQ Quiz in मल्याळम - Objective Question with Answer for Set Theory and types of Sets - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക
Last updated on Mar 12, 2025
Latest Set Theory and types of Sets MCQ Objective Questions
Top Set Theory and types of Sets MCQ Objective Questions
Set Theory and types of Sets Question 1:
If |A| = 50, |A ∩ B| = 45 and |B| = 48, then what is |P(A − B)|?
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 1 Detailed Solution
Concept Used:
P(A) represents the Powerset of A i.e., the set of all subsets of A.
|P(A)| = 2|A|
A - B = {x| x ∈ A and x ∉ B}
Calculation:
|A| = 50, |A ∩ B| = 45 and |B| = 48
⇒ A and B have 45 elements in common.
Hence, A - B must have only 5 elements i.e., |A - B| = 5
Hence, |P(A − B)| = 2|(A − B)| = 25
Set Theory and types of Sets Question 2:
If A = {1, 2, 5, 7} and B = {2, 4, 6} then find the number of proper subsets of A Δ B ?
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 2 Detailed Solution
CONCEPT:
Symmetric Difference of Sets:
Let A and B be two sets. The symmetric difference of sets A and B is the set (A - B) ∪ (B - A) and is denoted as A Δ B i.e A Δ B = (A - B) ∪ (B – A).
Note: If A is a non-empty set such that n(A) = m then number of proper subsets of A is given by 2m - 1.
CALCULATION:
Given: A = {1, 2, 5, 7} and B = {2, 4, 6}
First let's find out A - B and B - A
⇒ A - B = {1, 5, 7} and B - A = {4, 6}
As we know that, A Δ B = (A - B) ∪ (B – A)
⇒ A Δ B = {1, 5, 7} ∪ {4, 6} = {1, 4, 5, 6, 7}
As we can see that, the number if elements present in A Δ B = 5 i.e n(A Δ B) = 5
As we know that, if A is a non-empty set such that n(A) = m then number of proper subsets of A is given by 2m - 1.
So, the number of proper subsets of A Δ B = 25 - 1 = 31
Hence, the correct option is 3.
Set Theory and types of Sets Question 3:
If set A = {1, 3, 5, 7}, set B = {1, 4, 7}, find the value of A − B.
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 3 Detailed Solution
Concept use:
A - B = The element which are present in A but not in B
Calculations:
If set A = {1, 3, 5, 7}, set B = {1, 4, 7},
The Value of A - B = {3, 5} (The element which are present in A but not in B)
Set Theory and types of Sets Question 4:
If A = {1, 2, 3, 4} and B = {x ∈ N : x ≤ 5} then which of the following is true
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 4 Detailed Solution
Concept:
Subset: Let A and B be two sets. If every element of A is present in set B then A is called subset of B and it is denoted as A ⊆ B.
Equal Sets: Any two sets are said to be equal sets if and only if they are equivalent and as well as their elements are same.
Calculation:
Given: A = {1, 2, 3, 4} and B = {x ∈ N : x ≤ 5}
The set B can be re-written as B = {1, 2, 3, 4, 5}
As we know that, if A and B are two sets such that every element of A is present in set B but there is one element in B which is not present in A then A is a proper subset of B and is denoted as A ⊂ B
As we can see that, all the elements of set A are present in B but we have 5 ∈ B but 5 ∉ A ⇒ A ⊂ B
Hence, option 1 is the correct answer.
Set Theory and types of Sets Question 5:
If A = {λ, {λ, μ}}, then the power set of A is
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 5 Detailed Solution
Concept:
Power set: Let A be a non-empty set. Then, \(P\left( A \right) = \left\{ {B\;|\;B\; \subseteq A} \right\}\) is called as the power set of A.
For any non-empty set A with n(A) = x. Then the total no. of subsets of set A is given by: 2x.
i.e n(P(A)) = 2x.
Calculation:
Given: A = {λ, {λ, μ}}
Subsets of A are: {λ}, {{λ, μ}}, {λ, {λ, μ}}, φ
Power set of A, P(A) = {φ, {λ}, {{λ, μ}}, {λ, {λ, μ}}}Set Theory and types of Sets Question 6:
20 teachers of a school either teach Mathematics or Physics. 12 of them teach Mathematics while 4 teach both the subjects. Then, the number of teachers teaching Physics only is:
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 6 Detailed Solution
Concept Used:
\(n(A ∪ B)=n(A)+n(B)-n(A ∩ B)\)
Calculation:
let n(M) be the number of teachers who can teach mathematics and n(P) be the number of teachers who can teach physics.
Given: n(M ∪ P) = 20, n(M ∩ P) = 4, n(M) = 12
We have to calculate no of teachers who can only teach physics i.e., n(P) - n(P ∩ M)
Now, n(P ∪ M) = n(P) + n(M) - n(P ∩ M)
⇒ 20 = n(P) + 12 - 4
⇒ n(P) = 20 - 8 = 12
But this represents the total number of teachers teaching Physics, including those who teach both subjects. To find the number of teachers who teach only Physics, we subtract those who teach both subjects:
⇒ n(P) - n(P∩M) = 12 - 4 = 8
Hence, the number of teachers who can only teach physics is 8.
Set Theory and types of Sets Question 7:
If A, B and C are non-empty sets, then (A - B) ⋃ (B - A) equals
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 7 Detailed Solution
Concept:
- A ⋃ B denotes the elements which are in set A or set B.
- A ∩ B denotes the elements which are in both set A and set B.
- A-B denotes the elements which are only in set A and not in B.
- B-A denotes the elements which are only in set B and not in set A.
Calculation:
As it can be seen from the Venn diagram the purple area is (B - A) and the orange area is (A - B).
The green area is (A ∩ B) and all three of those areas together are (A ⋃ B).
It can be seen that (A - B) ⋃ (B - A) is the orange and the purple areas together.
This can also be found in the difference between (A ⋃ B) and (A ∩ B).
Hence, (A - B) ⋃ (B - A) = (A ⋃ B) - (A ∩ B)
Set Theory and types of Sets Question 8:
If A = {1, a, 3}, then find the power set of A ?
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 8 Detailed Solution
Concept:
Let A be set, then the set of all the possible subsets of A is called the power set of A is called the power set of A and is denoted by P(A) = {X : X ⊆ A}
Calculation:
Given: A = {1, a, 3}
⇒ the subsets of A are: ϕ, {1}, {a}, {3}, {1, a}, {1, 3}, {a, 3}, A
As we know that,
The power set of A is given by P(A) = {X : X ⊆ A}
⇒ P(A) = {ϕ, {1}, {a}, {3}, {1, a}, {1, 3}, {a, 3}, A}
Hence, option 1 is correct.
Set Theory and types of Sets Question 9:
If A = { x : x is a multiple of 3} and B = (x : x is a multiple of 4} and C = {x : x is a multiple of 12}, then which one of the following is a null set?
where A \ B: Set A with the elements that are not in set B removed. This is also known as the set difference between A and B.
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 9 Detailed Solution
Concept:
- Null set is the set that does not contain anything.
- In mathematical sets, the null set, also called the empty set,
- It is symbolized or { }.
Calculation:
Given:
A = {x : x is a multiple of 3}
∴ A = {3, 6, 9, 12, 15, 18, 24…}
B = {x : x is a multiple of 4}
∴ B = {4, 8, 12, 16, 20, 24, 28, 32 ...}
C = {x : x is a multiple of 12}
∴ C = {12, 24, 36, 48, 60, 72, 84, 96 ...}
Now,
A∩B = {12, 24 ...} = C
∴ (A∩B) \ C = { } = Null set
Set Theory and types of Sets Question 10:
If A = {0, 1, 2, 4} and B = {1, 3, 5} then (A - B) x (A \(\cap \) B) =
Answer (Detailed Solution Below)
Set Theory and types of Sets Question 10 Detailed Solution
Given:
A = {0, 1, 2, 4} and B = {1, 3, 5}
Calculation:
(A - B) = {0, 2, 4}
(A \(\cap \) B) = {1}
Now (A - B) x (A \(\cap \) B) = {0, 2, 4} × {1}
⇒ {(0, 1), (2, 1), (4, 1))}
Hence the correct answer is "{(0, 1), (2, 1), (4, 1)}"