MATH SOLVE

2 months ago

Q:
# Consider the sets A={n e P:n is odd} B = {n e P:n is prime) C = {4n +3:n β¬ P} D = {x e R : x2 - 8x + 15 = 0} Which of these sets are subsets of which? Consider all 16 possibilities.

Accepted Solution

A:

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 areA={n β P:n is odd}B = {n β P:n is prime)C = {4n +3:n β P}D = {x β R : xΒ² - 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 areA = {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]