Question

if p=(3m:m£n ) and q=(3^n:n£n) then what is the relation between p and q?​

Answer 1

Complete question:

If p = (3m : m ∈ N) and q = (3ⁿ : n ∈ N) then what is the relation between p and q?​

(a) p ⊂ q (b) q ⊂ p (c) p = q (d) p ⊂ q = N

The correct answer to this question is option (b) q ⊂ p

Given:

p = (3m : m ∈ N) and

q = (3ⁿ : n ∈ N)

To find:

The relationship between p and q =?

Solution:

It is given that p = (3m : m ∈ N) and q = (3ⁿ : n ∈ N)

Both sets p and q are given in the set builder form.

We need to change them into the listing form.

N is the set of natural numbers.

N = {1, 2, 3, 4, 5...n natural numbers}

p = (3m : m ∈ N)

If m = 1, 2, 3, 4,...

p = {3×1, 3×2, 3×3, 3×4,...}

p = {3, 6, 9, 12,...}

q = (3ⁿ : n ∈ N)

If n = 1, 2, 3, 4,...

q = {3¹, 3², 3³, 3⁴,...}

q = {3, 9, 27, 81,...}

All the elements of set q belong to set p. So, we can say that set q belongs to set p or set q is the subset of set p.

The correct answer to this question is option (b) q ⊂ p

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