Are these 2 different questions or is this one equation
Answer:
Consider f: N → N defined by f(0)=0 and f(n)=n-1 for all n>0.
Step-by-step explanation:
First we will prove that f is surjective. Let y∈N be any natural number. Define x as the number x=y+1. Then x∈N, and f(x)=x-1=(y+1)-1=y. We conclude that f is surjective.
However, f is not injective. Take x1=0 and x2=1. Then x1≠x2 but f(x1)=0 and f(x2)=x2-1=1-1=0. We have shown that there are two natural numbers x1,x2 such that x1≠x2 but f(x1)=f(x2), that is, f is not injective.
Note:
If 0∉N in your definition of natural numbers, the same reasoning works with the function f: N → N defined by f(1)=1 and f(n)=n-1 for all n>1. The only difference is that you consider x1=1, x2=2 for the injectivity.
Answer:
Third option
Step-by-step explanation:
The first definition is not as broad as it should be, therefore, while an angle does meet that criteria, it's not a general definition, hence, it is incorrect. The second one is incorrect as well because a parabola has a vertex, and it is certainly not an angle. This definition is not specific enough, so it will be eliminated. The last one is again, too specific. The third one is the best answer because it is broad enough while still being specific.
Answer:
"For every 6 windows I wash, I earn $2."
The ratio of windows washed to money earned is 3:1.
"For every 5 baseballs sold at the store, 7 footballs are sold."
The ratio of baseballs sold to footballs sold is 5:7
