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.

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.

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