COMEDK · Maths · 17. Mathematical Reasoning
The set of all integral multiples of \(5\) is a subgroup of
- A The set of all rational numbers under multiplication
- B The set of all integers under multiplication
- C The set of all non-zero rational numbers under multiplication
- D The set of all integers under addition
Answer & Solution
Correct Answer
(D) The set of all integers under addition
Step-by-step Solution
Detailed explanation
Let \(H\) consist of the integral multiple of 5 , i.e. \[ H=\{5 x: x \in I\} \] This \(H\) is the non-empty subset of \(I\). Now, let \(a=5 r\) and \(b=5 \mathrm{~s}\) any two elements of \(H\), where \(r\) and \(s\) are some integers. We have, \(a+b=5 r+5 s=5(r+8) \in H\).…
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