Let Z be the set of all integers and let A 0 = { n ∈ Z | n = 4 k , for some integer k } A 1 = { n ∈ Z | n = 4 k + 1 , for some integer k } A 2 = { n ∈ Z | n = 4 k + 2 , for some integer k } and A 3 = { n ∈ Z | n = 4 k + 3 , for some integer k } Is { A 0 , A 1 , A 2 , A 3 } a partition of Z? Explain your Is { A 0 , A 1 , A 2 , A 3 } a partition of Z ? Explain your answer.
Let Z be the set of all integers and let A 0 = { n ∈ Z | n = 4 k , for some integer k } A 1 = { n ∈ Z | n = 4 k + 1 , for some integer k } A 2 = { n ∈ Z | n = 4 k + 2 , for some integer k } and A 3 = { n ∈ Z | n = 4 k + 3 , for some integer k } Is { A 0 , A 1 , A 2 , A 3 } a partition of Z? Explain your Is { A 0 , A 1 , A 2 , A 3 } a partition of Z ? Explain your answer.
Solution Summary: The author explains that leftA0,A1,A2,A3right is a partition of Z.
Let Z be the set of all integers and let
A
0
=
{
n
∈
Z
|
n
=
4
k
,
for
some integer
k
}
A
1
=
{
n
∈
Z
|
n
=
4
k
+
1
,
for
some integer
k
}
A
2
=
{
n
∈
Z
|
n
=
4
k
+
2
,
for
some integer
k
}
and
A
3
=
{
n
∈
Z
|
n
=
4
k
+
3
,
for
some integer
k
}
Is
{
A
0
,
A
1
,
A
2
,
A
3
}
a partition of Z? Explain your Is
{
A
0
,
A
1
,
A
2
,
A
3
}
a partition of Z? Explain your answer.
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MFCS unit-1 || Part:1 || JNTU || Well formed formula || propositional calculus || truth tables; Author: Learn with Smily;https://www.youtube.com/watch?v=XV15Q4mCcHc;License: Standard YouTube License, CC-BY