Find domain and range of relation : $\;R=\{ (a , b)\in\Bbb N\times\Bbb R^+\; :\; ⌊b⌋ −2 \le a\le⌊b⌋+2 \}\;$. $\Bbb R^+\;$ means real positive numbers and $\;\Bbb N\;$ natural numbers
Can someone explain it ? My teacher said something like you put a=b in this and there comes domain as Natural numbers? I dont understand this... I know for a fact that if we have Relation like <1,5> <4,6> then domain is 1,4 and range is 5,6 but I dont understand how to calculate this in this case...
In your question: $R=\{(a,b)∈\Bbb N×\Bbb R^+:⌊b⌋−2≤a≤⌊b⌋+2\} $ The first part: $(a,b)∈\Bbb N×\Bbb R^+$ means that a belongs to natural numbers and b belongs to positive real numbers.
So we can first limit the domain (values of a) to Natural numbers and range (values of b) to Real positive numbers.
But that is not enough to find the actual domain as a and b must also satisfy the condition given. However in your case... $b∈\Bbb R^+$ so $b∈(0,∞)$ so for a also $a∈[0,∞)$ but only natural numbers.
So your domain is natural numbers and range is positive real numbers.