COMEDK · Maths · 20. Sets and Relations
If \(P=\{5 m: m \in N\}\) and \(Q=\left\{5^m: m \in N\right\}\), where \(N\) is set of natural numbers, then
- A \(Q \subset P\)
- B \(P=Q\)
- C \(P \subset Q\)
- D \(P \cup Q=N\)
Answer & Solution
Correct Answer
(A) \(Q \subset P\)
Step-by-step Solution
Detailed explanation
The set \(P\) is defined as \(P = \{5m : m \in N\} = \{5, 10, 15, 20, 25, 30, \dots\}\). The set \(Q\) is defined as \(Q = \{5^m : m \in N\} = \{5^1, 5^2, 5^3, \dots\} = \{5, 25, 125, 625, \dots\}\). Comparing the elements of \(P\) and \(Q\), we observe that every element of…
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