Respuesta :
Answer:
[tex]A\subset A, B\subset B,C\subset C,D\subset D[/tex],[tex]A\subset B[/tex], [tex]D\subset A[/tex] and [tex]D\subset B[/tex].
Step-by-step explanation:
The given sets are
A={n ∈ P:n is odd}
B = {n ∈ P:n is prime)
C = {4n +3:n ∈ P}
D = {x ∈ R : x² - 8x + 15 = 0}
P is the set of prime numbers and R is the set of real numbers.
[tex]x^2 - 8x + 15 = 0[/tex]
[tex]x^2 - 5x-3x + 15 = 0[/tex]
[tex]x(x-5)-3(x-5) = 0[/tex]
[tex](x-5)(x-3) = 0[/tex]
So, the elements of all sets are
A = {3, 5, 7, 11, 13, 17, 19, 23, ...}
B = {2, 3, 5 , 7, 11, 13, 17, 19, 23, ...}
C = {11, 15, 23, ...}
D = {3,5}
Each sets is a subset of it self. So,
[tex]A\subset A, B\subset B,C\subset C,D\subset D[/tex]
All the elements of A lie in set B, so A is a subset of B.
[tex]A\subset B[/tex]
Since [tex]15\notin A[/tex] and [tex]15\notin B[/tex], So, C is not the subset of A and B.
D has two elements, 3 and 5, Since [tex]3,5\in A[/tex] and [tex]3,5\in B[/tex], therefore
[tex]D\subset A[/tex] and [tex]D\subset B[/tex]
