1. determine whether the following statements are true or false.
if they are true to prove them if they are false to provide a counterexample.
(a) the difference between any two odd integers is even.
(b) if and are integers and + is even, then either is even or is even.
(c) if is odd and is even, then + is odd.

Step-by-step explanation:

a) True. Let I integer = 2m+1 and second integer 2n+1

Difference = 2(m-n) hence even

b)False. If m and n are integers and m+n is odd then either both even or both odd

Eg: 3 and 5.  3+5 =8 is even but both are even

c) True

m is odd then m= 2n+1

l is even so l = 2p

Sum = 2(n+p)+1  hence odd

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.

false

step-by-step explanation:

the meaning of changing is to edit or make something different.

but transmitting means cause (something) to pass on from one place or person to another.

there 2 different things