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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) is ______.
Options
34
41
33
30
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Solution
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) is 41.
Explanation:
Given that, S = {x|x is a positive multiple of 3 < 100}
∴ S = {3, 6, 9, 12, 15, 18, ..., 99}
⇒ n(S) = 33
T = {x|x is a prime number < 20}
∴ T = {2, 3, 5, 7, 11, 13, 17, 19}
⇒ n(T) = 8
So, n(S) + n(T)
= 33 + 8
= 41
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