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# IST 230 Section 003 Extra Credit 1. Prove that if an integer n is positive and a perfect square, then n+2 is not a perfect square. Define the...

This is for IST 230 a course about Language, Logic, and Discrete Mathematics.

I need 8/10 (80%) on this extra credit assignment to get credit, and if I get credit my grade will go from a 88 to a 90 so if you don't know it please don't take the question as I will not accept a bad answer.

IST 230 Secton 003 Ex±ra Credi± 1. Prove ±ha± if an in±eger n is positve and a perfec± square, ±hen n + 2 is no± a perfec± square. 2. DeFne ±he following se±s: A = { x Z : x iseven } B ={ x R : x≥ 1 } C = { 3,1,2,6,7,9 } D ={ 2,3,5,9,10,17 } Indica±e whe±her ±he following s±a±emen±s are ±rue or false. a. π B b. A B c. C B d. 8 A∩B e. A ∩C B f. C A B g. A ∩C∩D = h. | C |= ¿ D ¿ i. | C∩D |= 3 3. Is i± possible ±o have a relaton on a se± ±ha± is symme±ric and ant-symme±ric? If no±, explain why. If so, give an example. 4. Give ±he summaton no±aton for ±he following sums. a. The sum of ±he cubes of ±he Frs± 15 positve in±egers. b. (− 2 ) 5 +(− 1 ) 5 + + 7 5 c. The sum of ±he squares of ±he odd in±egers be±ween 0 and 100
5. Prove that any postage of 8 cents or more can be made from 5 cent or 3 cent stamps. 6. Group the following according to equivalence mod 11. That is, put two numbers in the same group if they are equivalent mod 11. {− 110, 93, 57,0,17,108,130,232,1111 } 7. Give the decimal representa±on for the following numbers: a. ( 1101010 ) 2 b. ( 364 ) 7 c. ( A 3 ) 16 8. Ten members of a wedding party are lining up in a row for a photograph. a. How many ways are there to line up the 10 people? b. How many ways are there to line up the 10 people if the groom must be to the immediate leF of the bride in the photo? c. How many ways are there to line up the 10 people if the groom must be next to the bride (on either her leF of right side)? 9. A round robin tournament is one where each player plays each of the other players exactly once. Prove that if no person loses all his games, then there must be two players with the same number of wins. 10. Prove that these two graphs are isomorphic:

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