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.
Answer:
Step-by-step explanation:
<u>Factored form of a parabola</u>
where:
- p and q are the x-intercepts.
- a is some constant.
Given x-intercepts:
Therefore:
To find a, substitute the given point (4, 8) into the equation and solve for a:
Therefore, the equation of the parabola in factored form is:
Expand so that the equation is in standard form:
The attached graph represents the graph of f(x) = (x - 1)^2 - 2
<h3>How to plot the graph?</h3>
The equation is given as:
f(x) = (x - 1)^2 - 2
Next, we set x to -2, -1, 0, 1 and 2.
So, we have:
f(-2) = (-2 - 1)^2 - 2 = 7
f(-1) = (-1 - 1)^2 - 2 = 2
f(0) = (0 - 1)^2 - 2 = -1
f(1) = (1 - 1)^2 - 2 = -2
f(2) = (2 - 1)^2 - 2 = -1
This means that the table of values is
x f(x)
-2 7
-1 2
0 -1
1 -2
2 -1
Next, we plot the above points and connect them.
See attachment for the graph of f(x) = (x - 1)^2 - 2
Read more about graphs and functions at:
brainly.com/question/4025726
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Answer:
0
Step-by-step explanation:
x and x are same terms.
