Question

The number of natural numbers less than 400 that are not divisible by 17 or 23 is :​

Answer 1

Answer:

371

Step-by-step explanation:

let A =natural numbers <400 divisible by 17

let B =natural numbers <400 divisible by 23

since 17 is prime n(A) =23 ----17*23 =391<400

since 23 is prime n(B) =17 ----17*23 =391<400

n(A∩B) =divisible by both 17 and 23. =1. i.e 391

n(AUB)=n(A)+n(B)−n(A∩B)=

=17+23-1​=39

you want ---Total-n(AuB) =n(s)-n(AuB) =400-39 =371

Answer 2

HERE IS YOUR ANSWER MATE!

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let A =natural numbers <400 divisible by 17

let B =natural numbers <400 divisible by 23

since 17 is prime n(A) =23 ----17*23 =391<400

since 23 is prime n(B) =17 ----17*23 =391<400

n(A∩B) =divisible by both 17 and 23. =1. i.e 391

n(AUB)=n(A)+n(B)−n(A∩B)=

=17+23-1​=39

you want ---Total-n(AuB) =n(s)-n(AuB) =400-39 =371

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I HOPE IT HELPS!

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