OurWay Pizza makes only two kinds of pizza, pepperoni and vegetarian. Any pizza
ID: 3792120 • Letter: O
Question
OurWay Pizza makes only two kinds of pizza, pepperoni and vegetarian. Any pizza of either kind comes with an even number of breadsticks (not necessarily the same even number for both kinds). Any order of 2 or more pizzas must include at least 1 of each kind. When the delivery driver goes to deliver an order, he or she puts the completed order together by combining 2 suborders-picking up all the pepperoni pizzas from 1 window and all the vegetarian pizzas from another window. Prove that for a delivery of n pizzas, n greaterthanorequalto 1, there are an even number of breadsticks included.Explanation / Answer
I am going to prove this using Proof By Contradiction
Given,
a) OurWay delivers only 2 kinds of Pizza, lets say Pepparoni as 'P' and Veg as 'V'.
b) Either of P or V contains even number of Bread sticks ie,
P = b1 = 2 * q
V = b2 = 2 * q and (b1 != b2 || b1== b2) and q>=1 ---------- (i)
b1 = no. of breads in P, b2 = no. of breads in V
c) An order of n (n>=2) items must contains n= P + V where P>= 1 and V>=1 ---- (ii)
Let us assume that the order n = 1 contains odd number of breads. ----- (iii)
From the given hypothesis let us prove the no of breads contains when order n = 1, ie, when order n = 1 then it contais only one item either P or V. from (i) P = b1 which contains even number of breads. thefore the order with n=1 contains even number of breads which proves our assumption as wrong.
Let us assume that the order n = 2 contains odd number of breads. ------ (iv)
if n = 2, from (ii) we know that n = P + V ----> V = 1 and P = 1.
if V = 1, then it contains b2 no. of breads which is an even number according to (i)
if P = 1, then it contains b1 no. of breads which is an even number according to (i)
And order of 1 P and 1 V contains b1 + b2 number of breads which is even, Hence the order n = 2 contains even number of breads which makes our assumption wrong.
Hence when order = n items then n = xP + yV where (x+y = n),
when P and V contains even number of breads, x * P (x > = 1) conatins Even number of breads and y * V (y >= 1) also conatins Even number of breads, Hence n = xP + yV also contains even number of breads which proves our assumption wrong.
Hence from the proof of contradiction we can prove the the order n >=1 contains even number of breads
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.