Question

Let S = p q and E = {0, −2, 2, −4, 4, −6, 6, · · · } be the set of even integers. . Prove that |S| = |E| by constructing a bijection from S to E.

Answer 1

prove that | S | = | E | ; every element of S there is an Image on E , while not every element on E has an image on S

Step-by-step explanation:

Given that S = p, q are prime numbers greater than 0

E = {0, −2, 2, −4, 4, −6, 6, · · · }

To prove by constructing a bijection from S to E

detailed solution attached below

After the bijection :

prove that | S | = | E | : every element of S there is an Image on E , while not every element on E has an image on S

∴ we can say sets E and S are infinite sets