Discrete Structures Questions There are 8 questions, I need the solutions with the answer.Both hand written and computer answers are okay. Discrete Structu

Discrete Structures Questions There are 8 questions, I need the solutions with the answer.Both hand written and computer answers are okay. Discrete Structures Test 3
Show all your work and put your name at the top of each page
1) Compute the positive powers of 3 (from 0 to 7) in Z5 and in 26
2) Your list for 26 may seem to violate Fermat’s Little theorem but it does not. Why not?
3) Compute the following
a) 1774 mod 75 =
b) 314 mod 5 =
c) 2736 mod 36 =
4) Use Truth Tables to show that p q is equivalent to (p1-9) VGp Aq)
5) Suppose on the first day of face to face classes I say “If there is no parking in the lot by James Hall, then I
will be late for class” but on the second day of class there is no parking but I am on time. Did my actions
reflect my statement according to the Truth Table for Implies? Write down just the row of the truth table for
Implies that this situation represents.
6) Which of the following statements are true and which are false? Explain why.
a) Vx € Z(3y € Z((x = 2y)V(x = 3y)))
b) Vx € R(3y R(y = vw))
c) Vx E ZEy E Z(y = x²))
7) Each of the following expressions represents a statement about the integers. Using p(x) for “x is prime,”
q(x, y) for “x = y2″, r(x, y) for “x < y," s(x, y, z) for “z=xy,” and t(x, y) for “x=y," determine which expressions represent true statements and which represent false statements. a) Vx e z+(By Z+(r(x, y) 19(x, y))) b) Vx € Z+(Vy E Z+(q(x, y) =r(x,y))) c) Vx Z(vy ez (vz e z((s(x,y,z) At(x,y)) = a(z,y))) 8) Write a quantified statement for the zero-product rule. You may use p(x) for "(x + a)(x + b) = 0," q(x) for “(x + a) = 0,” f(x) for “(x + b) = 0," and you may take as given that a and b are Real numbers. Purchase answer to see full attachment