Question

Write In Set Builder Form A={ 5,7}​

Answer 1

Answer:

{x:x is a odd number 4<x<8}

Answer 2

Answer:

write the terms as,

1=2(1)&#x2212;13=2(2)&#x2212;15=2(3)&#x2212;17=2(4)&#x2212;19=2(5)&#x2212;1" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: 400; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: 0px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(51, 46, 43); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;">1=2(1)−13=2(2)−15=2(3)−17=2(4)−19=2(5)−11=2(1)−13=2(2)−15=2(3)−17=2(4)−19=2(5)−1

And so on. Now, here we can notice from the representation of each element that they can be expressed in the form of 2n - 1, where the value of n starts from 1and as the number of elements in the set is not defined, so the value of n goes to infinity. So, we can say that the value n belongs to the natural number or we can write it as, n&#x2208;N" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: 400; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: 0px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(51, 46, 43); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;">n∈Nn∈N.

Hence, we can represent set G as {x:x=2n&#x2212;1,n&#x2208;N}" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: 400; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: 0px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(51, 46, 43); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;">{x:x=2n−1,n∈N}{x:x=2n−1,n∈N}.