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.
The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of children and y represent the number of adult, hence:
5.2x + 9.9y = 1303.5 (1)
Also:
x + y = 163 (2)
From both equations:
x = 66, y = 97
The number of tickets sold on Friday were 66 children tickets and 97 adult tickets.
Find out more on equation at: brainly.com/question/2972832
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Answer:
15.63 cm^3
Step-by-step explanation:
Assuming that the ice cube is a perfect cube, then all of the sides are equal. There for, each side is 2.5 cm.
v = l*w*h
v = 2.5 * 2.5 * 2.5
v = 6.25 * 2.5
v = 15.625 cm^3
Answer:
Step-by-step explanation:
This represents an arithmetic progression with the first term of a = 15 and common difference of d = 3.
<u>The tenth row is the 10th term:</u>
<u>The row 10 has:</u>
- a₁₀ = 15 + 9*3 = 15 + 27 = 42 seats
