Question

Let s = {x : x is a positive multiple of 3 less than 100}, p = {x:x is a prime number less than 20}. then n(s) + n(p)

Answer 1

s={6,9,12,15,18,21,24,27,30,33,3639,42,45,48,51,54,57,60,63,66,69,72,75,78,81,84,87,90,93,96 ,99}
therefore,
n(s)=32
&
p={2,3,5,7,11,1317,19}
therefore,
n(p)=8
therefore,
n(s)+n(p)=32+8
=40

Answer 2

Answer:

41

Step-by-step explanation:

Given,

s = {x : x is a positive multiple of 3 less than 100}

⇒ s = { 3, 6, 9, 12,.............. 99 }

Since, 3, 6, 9, .....99 is an A.P.

Having the first term, a = 3,

Common difference, d = 3

Let n be the number of terms,

⇒ Last term, l = a + ( n - 1 ) d = 3 + ( n - 1 ) 3

⇒ 3 + ( n - 1 ) 3 = 99 ⇒ 3 + 3n - 3 = 99 ⇒ 3n = 99 ⇒ n = 33,

Thus, Number of elements in set S , n(s) = 33

Now, p = {x:x is a prime number less than 20}

⇒ p = { 2, 3, 5, 7, 11, 13, 17, 19 }

Thus, Number of elements in set P , n(p) = 8,

Hence, n(s) + n(p) = 33 + 8 = 41