Which is Q={x:x∈N, x<20, x is divisible by neither 2 nor 3}?
Answer and explanation
Correct answer: Q={1,5,7,11,13,17,19}
The governing concept is filtering a set by simultaneous non-divisibility conditions. Assuming N={1,2,3,...}, first consider 1 through 19. Remove every even number because it is divisible by 2, and remove 3, 9, and 15 because they are divisible by 3. The numbers left are 1, 5, 7, 11, 13, 17, and 19. Option C wrongly keeps multiples of 3, and D lists evens. Thus A is correct.
Frequently asked questions
What is the correct answer to this question?
Q={1,5,7,11,13,17,19}
Why is this the correct answer?
The governing concept is filtering a set by simultaneous non-divisibility conditions. Assuming N={1,2,3,...}, first consider 1 through 19. Remove every even number because it is divisible by 2, and remove 3, 9, and 15 because they are divisible by 3. The numbers left are 1, 5, 7, 11, 13, 17, and 19. Option C wrongly keeps multiples of 3, and D lists evens. Thus A is correct.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems.
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