1-If-A-and-B-are-sets-define-their-scheffer-product-A-B-by-A-B-A-B-Prove-by-definitions-that-A-B-A-B-A-B-2-State-the-strong-principle-of-mathematical-induction-Suppose-that-a-1-1-a-2-3-a

FacebookTweetPin

Question Number 135889 by Ar Brandon last updated on 16/Mar/21

$$1\mathrm{\setminus }\mathrm{If}\mathrm{A}\mathrm{and}\mathrm{B}\mathrm{are}\mathrm{sets}\mathrm{define}\mathrm{their}\mathrm{scheffer}\mathrm{product}\mathrm{A}\ast \mathrm{B}\mathrm{by}\mathrm{A}\ast \mathrm{B}=\mathrm{A}\ast \cap \mathrm{B}\ast$$$$\mathrm{Prove}\mathrm{by}\mathrm{definitions}\mathrm{that}(\mathrm{A}\ast \mathrm{B})\ast (\mathrm{A}\ast \mathrm{B})=\mathrm{A}\cup \mathrm{B}$$$$$$$$2\mathrm{\setminus }\mathrm{State}\mathrm{the}\mathrm{strong}\mathrm{principle}\mathrm{of}\mathrm{mathematical}\mathrm{induction}.$$$$\mathrm{Suppose}\mathrm{that}{\mathrm{a}}_1=1,{\mathrm{a}}_2=3$$$${\mathrm{a}}_{\mathrm{k}}={\mathrm{a}}_{\mathrm{k}-2}+{2\mathrm{a}}_{\mathrm{k}-1}\mathrm{for}\mathrm{all}\mathrm{natural}\mathrm{numbers}\mathrm{k}⩾3.\mathrm{Use}\mathrm{the}\mathrm{strong}\mathrm{principle}\mathrm{of}$$$$\mathrm{mathematical}\mathrm{induction}\mathrm{to}\mathrm{prove}\mathrm{that}{\mathrm{a}}_{\mathrm{n}}\mathrm{is}\mathrm{odd}\mathrm{for}\mathrm{all}\mathrm{natural}\mathrm{numbers}.$$

Answered by mindispower last updated on 19/Mar/21

$$A\ast B=\dots .?$$

Terms of Service
Privacy Policy
Contact: info@tinkutara.com

FacebookTweetPin