Consider the following proposition: For each integer a, a = 2 (mod 8) if and only if (a^2 + 4a) = 4 (mod 8).

(a) Write the proposition as the conjunction of two conditional statements.

(b) Determine if the two conditional statements in Part (a) are true or false. If a conditional statement is true, write a proof, and if it is false, provide a counterexample.

(c) Is the given proposition true or false? Explain.

hi im bob : l

step-by-step explanation:

i may be incorrect but i believe that her first error was in step one when she multiplyed her equation by 1/4 when she should have divided it by 1/4

not sure srry man

(a) x intercepts: -6 and 2

you can obtain these by solving the equation 0=x^2 +4x-12 using your favorite quadratic formula. but it is easy to verify -6 and 2 indeed satisfy this equation.

(b) y intercept: -12

this is obtained by setting x=0: 0^2+4*0-12 = -12

(c) the minimum value is: -16 (this is the vertex)

you can get the vertex by rewriting the equation into the form:

there is no global or local maximum as the function goes to infinity, so only in the limit sense: +infinity.