Need help with sets
1. (a) Let E denote the set of all even integers:
E = {2n I n E Z}.
Write the set
A= (1,00)nE
in descriptive notation.
(b) Write down 10 elements of the set
B = {p + q 1 p and q are prime numbers}.
(Recall that a natural number p is prime if it has exactly two divisors: 1 and p. So the prime numbers are 2, 3, 5, 7,11, ... )
(c) Prove that B g A.
(d) Which statement do you think is true: A C B or A g B? Give a brief explanation for your guess (but you do not need to give a proof).
(a) Sketch the graph of the function [-4, 4] -+ 11 given by y = cos(irx).
(b) Find the set
{x E [-4, 4] 1 cos(irx) 0}
and write it as a union of intervals.
(c) Find the set
{x E [-4, 4]
x + 1 }
0
x — 2
and write it as a union of intervals. (d) Find the set
{x E [-4, 4] (x + 1) cos(7x) 01 ex(x — 2)
and write it as a union of intervals.