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Counting numbers have fascinated human m...

Counting numbers have fascinated human mind from time immemorial. The first set he seems to have pondered about is the set of natural numbers, N Various subsets of this set were diffined. Note worthy among them are
Prime Number :- if a natural number has exactly two divisors it is called a prime number. Yet another way Simple examples are `2,3,5,7,...........`
`{2,3}` in the only set of consective primes.
Composite numbers :- A natural number having more than 2 divisors is called a composite number. Simple examples are `4,6,8,9,10,..........`
Note that 1 is neither prime nor composite.
Coprime or relatively prime numbers :- A pair of natural numbers is acalled a set of coprime numbers if their highest common factor (HCF) or greatest common divisor (g.c.d.) is 1. For example 8 & 5 are co-prime
Note that these two numbers need not be prime.
More over 1 is coprime with evert natural numbers.
a prime number is coprime with all natural numbers which are not it's multiple.
Twin Prime :- A pair of primes is called twin primes if their non-negative difference is '2' For example `{3,5} , {5,7}, (11,13}` , .........
Based on above difinitions solve that following problems
Number of prime numbers less than 10 is
`"(a) 2 (b) 3 (c) 4 (d) 5 "`

A

2

B

3

C

4

D

5

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Counting numbers have fascinated human mind from time immemorial. The first set he seems to have pondered about is the set of natural numbers, N Various subsets of this set were diffined. Note worthy among them are Prime Number :- if a natural number has exactly two divisors it is called a prime number. Yet another way Simple examples are 2,3,5,7,........... {2,3} in the only set of consective primes. Composite numbers :- A natural number having more than 2 divisors is called a composite number. Simple examples are 4,6,8,9,10,.......... Note that 1 is neither prime nor composite. Coprime or relatively prime numbers :- A pair of natural numbers is acalled a set of coprime numbers if their highest common factor (HCF) or greatest common divisor (g.c.d.) is 1. For example 8 & 5 are co-prime Note that these two numbers need not be prime. More over 1 is coprime with evert natural numbers. a prime number is coprime with all natural numbers which are not it's multiple. Twin Prime :- A pair of primes is called twin primes if their non-negative difference is '2' For example {3,5} , {5,7}, (11,13} , ......... Based on above difinitions solve that following problems Number of composite numbers less than 15 is "(a) 10 (b) 9 (c) 8 (d) 7"

Counting numbers have fascinated human mind from time immemorial. The first set he seems to have pondered about is the set of natural numbers, N Various subsets of this set were diffined. Note worthy among them are Prime Number :- if a natural number has exactly tow divisors it is called a prime number. Yet another way Simple examples are 2,3,5,7,........... {2,3} in the only set of consective primes. Composite numbers :- A natural number habing more than 2 divisors is called a composite number. Simple examples are 4,6,8,9,10,.......... Note that 1 is neither prime nor composite. Coprime or relatively prime numbers :- A pair of natural numbers is acalled a set of coprime numbers if their highest common factor (HCF) or greatest common divisor (g.c.d.) is 1. For example 8 & 5 are co-prime Note that these two numbers need not be prime. More over 1 is coprime with evert natural numbers. a prime number is coprime with all natural numbers which are not it's multiple. Twin Prime :- A pair of primes is called twin primes if their non-negative difference is '2' For example {3,5} , {5,7}, (11,13} , ......... Based on above difinitions solve that following problems Let p & q be the number of natural numbers which are less than or equal 20 and are prime & composite respectively, then 20-p-q is equal to "(a) 1 (b) 0 (c) 2 (d) 3"

Knowledge Check

  • If the replacement set is the set of natural numbers, then the solution of x le 3 is:

    A
    {0, 1, 2}
    B
    {1, 2, 3}
    C
    {1, 2}
    D
    {0, 1, 2, 3}
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