Answer:
(a) A = {... -23, -16, -9, -2, 5, 12, 19, 26, ....}
(b) [tex]A = {x\in Z: x = 5 - 7t,\ t\in Z}[/tex]
Solution:
For two integers x and y to be congruent, we know that:
If 't' divides y - x, we say that x is congruent to y modulo t, written x ≡ y mod t.
Now,
In roster form, we include each element in the representation of the set.
In set-builder form, we use mathematical notation and properties of the elements of the set.
Now,
As per the question;
(a) To represent all the integers congruent to 5 (mod 7) by roaster method of a set A (say):
where
[tex]x\in Z[/tex] such that
x ≡ 5 (mod 7)
Then
A = {... -23, -16, -9, -2, 5, 12, 19, 26, ....}
(b) In set builder form,
[tex]A = {x\in Z: x = 5 - 7t,\ t\in Z}[/tex]
