the set of positive integers less than 20 which are divisible by 5 in builder set form?
5, 10, 15
I do not know what a builder set is.
To find the set of positive integers less than 20 that are divisible by 5 in set-builder notation, we can follow these steps:
1. Determine the condition for an integer to be divisible by 5: An integer is divisible by 5 if its remainder when divided by 5 is zero.
2. Identify the set of positive integers less than 20: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19}.
3. Apply the condition to filter the integers: We need to select only those integers in the set for which the remainder is 0 when divided by 5.
The filtered set would be: {5, 10, 15}.
4. Write the set in set-builder notation: {x ∈ Z+ : x < 20, x mod 5 = 0}.
Therefore, the set of positive integers less than 20 that are divisible by 5 in set-builder form is {x ∈ Z+ : x < 20, x mod 5 = 0}.