Discrrete mathematics for computer science strong induction warmup

Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: on = Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: on = = Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: o n = = 3+5 is triquinqual on = Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases o n = = 3+5 is triquinqual on = Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases o n = = 3+5 is triquinqual o n = = 3+3+3 is triquinqual on = Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases o n = = 3+5 is triquinqual o n = = 3+3+3 is triquinqual o n = 10 = 5+5 is triquinqual o (I.H.) Assume Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases o n = = 3+5 is triquinqual o n = = 3+3+3 is triquinqual o n = 10 = 5+5 is triquinqual o (I.H.) Assume m ≥ 10 and every n≤m is triquinqual Prove Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases o n = = 3+5 is triquinqual o n = = 3+3+3 is triquinqual o n = 10 = 5+5 is triquinqual o (I.H.) Assume m ≥ 10 and every n≤m is triquinqual Prove m+1 is triquinqual Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases o n = = 3+5 is triquinqual o n = = 3+3+3 is triquinqual o n = 10 = 5+5 is triquinqual o (I.H.) Assume m ≥ 10 and every n≤m is triquinqual Prove m+1 is triquinqual o m+1 is triquinqual because m+1 = (m2)+3 and m-2 ≥ is triquinqual  ...Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n... • Proof: on = Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: on = = Warm-up Problem • Prove by induction: Every n≥8 is the sum of 3’s and... Problem • Prove by induction: Every n≥8 is the sum of 3’s and 5’s (“n is triquinqual”) • Proof: Need multiple base cases o n = = 3+5 is triquinqual on = Warm-up Problem • Prove by induction: Every