Please show work if needed, thank you! Which of these collections of subsets are
ID: 3690421 • Letter: P
Question
Please show work if needed, thank you!
Which of these collections of subsets are partitions of the set of integers? the set of even integers and the set of odd integers the set of integers divisible by 3. the set of integers leaving a remainder of 1 when divided by 3, and the set of integers leaving a remainder of 2 when divided by 3 the set of integers less than -100, the set of integers with absolute value not exceeding 100. and the set of integers greater than 100 the set of integers not divisible by 3, the set of even integers, and the set of integers that leave a remainder of 3 when divided by 6.Explanation / Answer
a) is true
because set of even numbers{0,2,4....} and {1,3,5..... }
if combine both sets{0,1,2,3,4,5} ==set of integers (we consider negative as well)
b)is true
set of integers divisible by 3 {0,3,6,9...}
set of integers divisible by 3 and leaves remainder 1 {1,4,7....}
set of integers divisible by 3 and leaves remainder 2 {2,5,8....}
Union of above 3 sets gives us set of integers.
c) Is also true
set of integers less than -100 {-101,-102....-inf}
set of integers absolute value not exceeding 100 {-inf....-1,0,1,2,3....100}
set of integers greater than 100 {101,102....inf}
Union of above three sets gives set of integers
d)false
set of integers not divisible by 3 {1,2,4,5,7,8......}
set of even integers {2,4,6,8}
set of integers leaves reminder 3 when divisible by 6 {3,9,15,21.....}
if we clearly observe some numbers example 19 does come anyof the above sets
so the combination cannot be integers.