Which option correctly gives N={x∈N: x<20 and x is divisible by both 4 and 5}?
Answer and explanation
Correct answer: N=∅
A number divisible by both 4 and 5 must be a multiple of their least common multiple. Since lcm(4,5)=20, every such positive natural number is at least 20; the first one is 20 itself. However, the condition requires x<20, so 20 is excluded and no natural number satisfies both conditions. Therefore N is the empty set, making option A correct. Options B, C and D fail the divisibility-and-bound test.
Frequently asked questions
What is the correct answer to this question?
N=∅
Why is this the correct answer?
A number divisible by both 4 and 5 must be a multiple of their least common multiple. Since lcm(4,5)=20, every such positive natural number is at least 20; the first one is 20 itself. However, the condition requires x<20, so 20 is excluded and no natural number satisfies both conditions. Therefore N is the empty set, making option A correct. Options B, C and D fail the divisibility-and-bound test.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Number Systems. Topic: General chapter practice.
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