4 quarts are in a single gallon
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.
Which of the following sets of ordered pairs does not define a function? {(−1,4),(0,4),(1,4),(2,4),(3,4)} { ( − 1 , 4 ) , ( 0 ,
Novay_Z [31]
Step-by-step explanation:
5 is not function because an x cannot map on 2 different y's
8 ÷ 0.001 = 8 000
a) 8 ÷ 0.0001 = 80 000
8 ÷ 0.001 = 8 000
b) 8 ÷ 0.01 = 800
8 ÷ 0.001 = 8 000
8 ÷ 1/10 = 8 ÷ 0.1 = 80
c)8 ÷ 0.01 = 8 000
