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.
 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
={1,2}=Finite=Countable
Hence,  is countable.
 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
={1,2,3,....}=N
Hence, is countable.
 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
=Z=Countable
Hence,  countable.
 countable.
Case 4:If A and B are both countably infinite sets.
Suppose A=N and B=Z
Then, =
= =Z
=Z
Hence, is countable.
 is countable.
Therefore, if A and B are countable sets, then  is also countable.
 is also countable.
 
        
                    
             
        
        
        
The percent markup is 40% cost: $2.50/hammer *40%=1.00 Cost+markup=3.50
 
        
             
        
        
        
Same side, interior angles of parallel lines cut by a transversal are supplementary.
The sum of the measures of supplementary angles is 180.
Angles 4 and 6 are same side, interior angles, so their measures add to 180.
m<4 + m<6 = 180
109 + m<6 = 180
m<6 = 180 - 109
m<6 = 71
Answer: m<6 = 71 deg.
        
             
        
        
        
621,864
Since the 4 is a smaller digit than a 5, the 6 in the tens place would stay the same while the 4 would become a 0.