Question

State the following sets are finite or infinite:

M = {r : r = `3/"n"`; n ∈ W and 6 < n ≤ 15}

Answer 1

M = {r : r = `3/"n"`; n ∈ W and 6 < n ≤ 15}

r = `3/"n"`

When n = 7, 
r = `(3)/(7)`

When n = 8, 
r = `(3)/(8)`

When n = 9, 
r = `(3)/(9)`

When n = 10, 
r = `(3)/(10)`

When n =11, 
r = `(3)/(11)`

When n = 12, 
r = `(3)/(12)`

When n = 13, 
r = `(3)/(13)`

When n = 14, 
r = `(3)/(14)`

When n = 15, 
r = `(3)/(15)`

∴ M = `{3/7, 3/8, 3/9, 3/10, 3/11, 3/12, 3/13, 3/14, 3/15}`

∴ It is a finite set.