MATHS [1 Mark Question Answer]

n(Q) = Factors of 16 are = 1. 2, 4, 8, 16
∴ n(Q) = 5

n(P) = Factors of 12 are
= 1, 2, 3, 4, 6, 12
∴ n(P) = 6

n (B) = {3, 6, 9, 12} = 4

(A – B) and n(A – B)
⇒ (A – B) = (2, 4, 8)
⇒ n(A - B) = 3

(A ∩ B) = {2, 4, 8}
n( A ∩ B) = 3

A∩B = {6}
n(A∩B) = 1

A ∪ B = {3, 4, 5, 7, 9, 10, 11}
n(A ∪ B) = 7

n(B) = (4, 7, 10) = 3

n(A) = (3, 5, 7, 9, 11) = 5

B-A
= [elements of set B which are not in set A]
= {10, 12}

A - B
= [elements of set A which are not in set B]
= {4, 5, 7}

A ∩ B
= [elements common to both the sets A and B]
= {6, 8}

A∪B
= [All the elements from set A and all the elements from set B]
= {4, 5, 6, 7, 8, 10, 12}

D = {even numbers less than 10} = {4, 6, 8}
D’ = {5, 7, 9, 10, 11, 12, 13}

C = {Prime numbers} = {5, 7, 11, 13}
C’ = { 4, 6, 8, 9, 10, 12}

B = {odd numbers greater then 8} = {9, 11, 13}
B’ = {4, 5, 6, 7, 8, 10, 12}

A = {even numbers} = {4, 6, 8, 10, 12}
A’= {5, 7, 9, 11, 13}

B = {p, q, r)
∴ subsets are : { } or φ, {p}, {q}, {r}, {p, q}, ip, r}, {q, r} and {p, q, r}

A = {a, c}
∴ Subsets are : { } or φ, {a}, {c} and {a, c}

E = {0} is not a proper subset of P.

D = {6, 5, 4} is not a proper subset of P.

C = {23, 45} is not a proper subset of P.

B = { } is a proper subset of P.

A = {3,4} is a proper subset of P.

F = (8, 7, 9, 5}
∴ F ⊂ A

E = { }
∴E ⊂ A (An empty set is subset of every set)

D = {7, 9, 10}
∴ D ⊄ A

C = {0}
∴ C φ A

B = {5, 8}
∴B ⊂ A

If each element of set P is also an element of set Q then P is said to be subject of Q; and Q is said to be super set of P.

φ and { } are the null sets other are not as there have same element.

P = {x : 3x = 0} which is not an empty set.

The set of lions in your class this is an empty set.

The set of triangles having three equal sides. This is not an empty set.

A = {0², 1², 2², 3², 4²} = {0, 1, 4, 9, 16} and B = {16, 9,4, 1, 0}.
These are equal sets as these have same and equal number of elements.

{x : x is a fan of cricket} and {x : x is a fan of football}
These are not disjoint sets as there can be a person who is fan of both the games.

{birds} and {tress}
These are disjoint sets as there is no common element in term.

Planets of the Solar system:
It is finite set as there are countable.

{x | x is a prime number between 7 and 10}:
As there is not such prime number between 7 and 10. Hence it is null set.

{coins used in India}:
∴ It is a finite set as these are countable.

{squares of natural numbers} :
∴ It is an infinite set.

{even numbers not divisible by 2} : It is a null set

{multiples of 8}: It is an infinite set.

Set of mountains in the world:
∴ It is an infinite set.

B = {x : x ∈ W ; x is less than 100}:
It is finite set as it has 100 elements i.e. from 0 to 99

A = {x : x is an integer between 1 and 2}
= It is a null set

{natural numbers more than 100}
= It is an infinite set.

G = {x : x is a perfect square number, x ∈N and x ≤ 30}:
n(G) = 5

F = {x : x ∈ Z and – 2 < x ≤ 5}
n(F) = 7

E = Set of prime numbers between 5 and 15:
n(E) = 3