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andre [41]
3 years ago
8

Will mark brainliest (scam links will be reported)

Mathematics
1 answer:
gregori [183]3 years ago
5 0

Answer:

30

hope it helps

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Give an example of a function f : N → N that is surjective but not injective. You must explain why your example is surjective an
Helen [10]

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.

7 0
3 years ago
Lucas is offered either 15% or $21 off his total shopping bill. how much would have to be spent to make the 15% option the best
vladimir1956 [14]
Let the total bill be x. We have:
<span>0.15x > 21 <-- Since 15% is 0.15     using inequality calc. x </span>>$140 
4 0
3 years ago
A tree grows 20 percent taller every year after it is planted. The tree was 12 feet tall when planted. How tall will it be after
Len [333]

Answer:

B.120 feet

Step-by-step explanation:

12 × 20 × 10 = 120

4 0
3 years ago
Anyone know what the answer to this is?
MariettaO [177]
It's the 3rd answer

1 \div (36a^{4}{b}^{10} )
8 0
3 years ago
Read 2 more answers
What is the sum of 4*8<br><img src="https://tex.z-dn.net/?f=4%20%5Ctimes%208" id="TexFormula1" title="4 \times 8" alt="4 \times
Inessa [10]
See picture reply for answer.

5 0
3 years ago
Read 2 more answers
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