If aa and bb are countable sets, then so is a∪ba∪b.

Answer with Step-by-step explanation:

We are given that A and B are two countable sets

We have to show that if A and B are countable then is countable.

Countable means finite set or countably infinite.

Case 1: If A and B are two finite sets

Suppose A={1} and B={2}

={1,2}=Finite=Countable

Hence, is countable.

Case 2: If A finite and B is countably infinite

Suppose, A={1,2,3}

B=N={1,2,3,...}

Then, ={1,2,3,....}=N

Hence, is countable.

Case 3:If A is countably infinite and B is finite set.

Suppose , A=Z={..,-2,-1,0,1,2,....}

B={-2,-3}

=Z=Countable

Hence, countable.

Case 4:If A and B are both countably infinite sets.

Suppose A=N and B=Z

Then,==Z

Hence, is countable.

Therefore, if A and B are countable sets, then is also countable.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl