Question

Write the set (1/2,2/3,3/4,4/5,5/6,6/7) in set - builder form .​

Answer 1

Step-by-step explanation:

i) {3,6,9,12}

={x:x=3n,nϵN and 1≤n≤4}

Alternatively, {x:x is a multiple of 3 and x≤12}

(ii) {2,4,8,16,32}

It can be seen that 2=2

1

,4=2

2

,8=2

3

,16=2

4

, and 32=2

5

.

∴{2,4,8,16,32}={x:x=2

n

,nϵN and 1≤n≤5}

(iii) {5,25,125,625}

It can be seen that 5=5

1

,25=5

2

,125=5

3

, and 625=5

4

.

∴{5,25,125,625}={x:x=5

n

,nϵN and 1≤n≤4}

(iv) {2,4,6,....}

It is a set of all even natural numbers.

∴{2,4,6,....}={x:x is an even natural number}

(v) {1,4,9,.....100}

∴{1,4,9...100}={x:x=n

2

,nϵN and 1≤n≤10}

Alternatively, {x:x is a square of natural number and x≤100}