One day, the Early Bird Restaurant used
1 answer:
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Answer:
Step-by-step explanation:
Given that there are 3 sets such that there are 100 elements in A1, 1000 in A2, and 10,000 in A3
a) If A1 ⊆ A2 and A2 ⊆ A3
then union will contain the same number of elements as that of A3
i.e.
b) If the sets are pairwise disjoint.
union will contain the sum of elements of each set
c) If there are two elements common to each pair of sets and one element in all three sets
We subtract common elements pairwise and add common element in 3
i.e.
<h3>Answer: Choice (b)</h3><h3>{ (1, 3), (3, 1), (4, 3) }</h3>
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Work Shown:
The notation "g o f" means g(f(x)). We have f(x) as the inner function that is computed first.
f(x) = { (1,2), (3,5), (4,1) }
The x coordinates of each point are: 1, 3, 4
The y coordinates are: 2, 5, 1
So the input x = 1 goes to y = 2 as the output. That output becomes the input of the g(x) function. Using x = 2 as the input for g, we see that 3 is the output. Check out the diagram below to see how each input goes into f, then goes into g to ultimately determine the x,y pairs. So far we've shown that x = 1 ultimately leads to y = 3.
Let's do another input: if x = 3 is plugged into f(x), then the output is 5 because of the point (3,5). Then x = 5 is plugged into g(x) to get x = 5 lead to y = 1. Ultimately x = 3 leads to y = 1 giving us (3,1) as another point.
Lastly, if x = 4 is plugged into f we get y = 1 as an output, which in turn is plugged into g to get 3 as the final output. The point (4,3) is the last ordered pair.
Again there's a lot to keep track of, so it helps to have a diagram as shown below.