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 ).

2 thoughts on “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 ).”

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

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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)

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