Suppose a finite number of players play a round-robin tournament, with everyone playing everyone else exactlyonce. each match has a winner and a loser (no ties). we say that the tournament has acycle of length mif there exist m players {p_1,p_2, . . ,p_m} such that p_1 beats p_2, who beats p_3, who beats p_m, who beats p_1. clearly this is possible only form ≥ 3.using mathematical induction, prove that if such a tournament has a cycle of length m, for some m≥3, then ithas a cycle of length 3.

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

c.

step-by-step explanation:

inverse operation of addition