Question

IF A = { x:x is a positive multiple of 3 less than 20 } and B = { x:x is a prime number less than 25 } THEN FIND n (A ) + n ( B ).

Answer 1

explanation

A={3,6,9,12,15,18}

B={2,3,5,7,11,13,17,19,23}

n(A)=6

n(B)=9

n(A)+n(B)=9+6=15

Answer 2

Question:-

If A = { x:x is a positive multiple of 3 less than 20 } and B = { x:x is a prime number less than 25 } Then find n (A ) + n ( B ).

Required Answer:-

Given:-

• A = {x:x is a positive multiple of 3 less than 20}
• B = { x:x is a prime number less than 25}

To Find:-

• n(A) + n(B)

Solution:-

Here,

A = {x:x is a positive multiple of 3 less than 20}

=> A = {3, 6,9,12,15,18}

Again,

B = { x:x is a prime number less than 25}

=> B = {2,3, 5, 7, 11, 13, 17, 19, 23}

Now,

The number of elements in a set is called the cardinal number, or cardinality, of the set. This is denoted as n(P), read “n of P” or “the number of elements in set P.”

Therefore,

n(A) = 6

n(B) = 9

∴ n(A) + n(B) = 6 + 9 = 15

Hence, the answer is 15

More Information:-

Symbol of sets:-

• { } = Set: a collection of elements
• A ∪ B = Union: in A or B (or both)
• A ∩ B = Intersection: in both A and B
• A ⊆ B = Subset: every element of A is in B.
• A ⊂ B = Proper Subset: every element of A is in B, but B has more elements.
• A ⊄ B = Not a Subset: A is not a subset of B
• A ⊇ B = Superset: A has same elements as B, or more
• A ⊃ B = Proper Superset: A has B's elements and more
• A ⊅ B = Not a Superset: A is not a superset of B
• A^c = Complement: elements not in A
• A − B = Difference: in A but not in B
• a ∈ A = Element of: a is in A
• b ∉ A = Not element of: b is not in A
• ∅ = Empty set
• U = Universal Set: set of all possible values (in the area of interest)
• P(A) = Power Set: all subsets of A
• A = B => Equality: both sets have the same members
• A×B = Cartesian Product (set of ordered pairs from A and B)