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Xq → p xq → p Which pairs of statements are logically equivalent?196 ContrapositiveProof 85SolutionsforChapter8 1Proposition Suppose n2ZIf 2 iseven,thenn iseven Proof (Contrapositive)Suppose nisnotevenThenn isodd,so ˘2a¯1 for someinteger a,bydefinitionofanoddnumberThusn 2 ˘(2 ¯1) 4 1 2(2a2¯2a)¯1Consequentlyn2 ˘2b¯1,whereb istheinteger2a2¯2a,son2 is odd Thereforen2 isnoteven ç 3Proposition Suppose a, b2ZIf 2( ¡2 )CSE 5311 Homework 1 Solution Problem 221 Express the function n3=1000 100n2 100n 3 in terms of notation Answer ( n3) Problem 233 Use mathematical induction to show that when nis an exact power of 2, the Htxzmelrjumy1m Ô‚¿‚á‚ñ ‚Ç‚ñ‚®‚è –XŽq •Ò‚Ý }