# hw3solsmc - Solutions to Homework 3 Math 2000 Notes Check...

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Solutions to Homework 3 - Math 2000 Notes: Check the back of the book for solutions to 2.1,2.5,2.9. 2.11 was done during tutorial. (# 2.2) Consider the sets A,B,C , and D deﬁned below. Which of the following state- ments are true? Give an explanation for each false statement. A = { 1 , 4 , 7 , 10 , 13 , 16 ,... } B = { x Z | x is odd } C = { x Z | x is prime and x 6 = 2 } D = { 1 , 2 , 3 , 5 , 8 , 13 , 21 , 34 , 55 ,... } . Solution . (a). Note that A may also be written as A = { n N | n = 3 x + 1 with x Z } . However, 25 = 3 · 8 + 1 and thus 25 A . Therefore 25 A is true. (b). Since 33 is odd, it follows that 33 D is true. (c). 22 / A D is false. Note that 22 = 3 · 7+1 and thus 22 A and hence 22 A D too. (d). C B is false since 7 C but 7 / B . (e). φ B D is false since φ is a subset but not an element of B D . (f) 53 / C is false since 53 is a prime number. (It suﬃces to check whether 53 is divisible by any primes

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hw3solsmc - Solutions to Homework 3 Math 2000 Notes Check...

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