Question

State which ofthe following sets are finite and which are infinite. Give reasons for your answer.
i. A={x: x ∈ N and x < 100}
ii. {x: x ∈ N and x≤5}
iii. C={1^2,2^2,3^2, ....}
iv. D={1,2,3,4}
v. {x: x is a day of the week}

Answer 1

i.Finite,A={1,2,3...99}n(A)=99
ii.Finite , The set ={1,2,3,4,5}n(?)=5
iii.Infinite,C={1²,2²,3²......infinity²}n(C)=Infinite
iv.Finite,D={1,2,3,4}n(D)=4
v.Finite, The set={Sunday,Monday,Tuesday,Wednesday,Thursday,Friday,Saturday}n(?)=7

Answer 2

I) Finite   ii) Finite  iii) Infinite iv) Finite   v) Finite

Step-by-step explanation:

Finite Sets: A set is said to be finite if all the elements in the set is countable when the set is expressed is roster form.

Infinite Sets: A set is said to be infinite if the elements in the set are uncountable, when the set is expressed in the roster form.

i)A={x: x ∈ N and x < 100}

So, A = {1, 2, 3, 4, ,,,,, 98,99}

So, A is finite.

ii){x: x ∈ N and x≤5}

Set = {1,2,3,4,5}

So, set is a finite set.

iii) C={1^2,2^2,3^2, ....}  = { 1, 4, 9, ...}

Since, the  elements can not be counted.

So, set is infinite.

(iv) D =(1,2,3,4}

D is a finite set.

v) {x: x is a day of the week}

Set = { Monday, Tuesday, Wednesday, ...., Sunday}

So, the elements are countable.

Set is finite.