n+1 2. Let an = (-1)"-for n > 1. (a) What is sup(fas, ab,...])? (b) What...
Let ne N. Show that Zn forn > 2 is not a group under multiplication as defined above. What happens for n = 1?
) Construct a context-free grammar for the language L={ ab”ab”a | n> > 1}.
Construct a context-free grammar for the language L={ ab”ab”a | n> 1}.
b. Let U2 u~xã. Show that E(b)=n-2 for n > 2. LU
11. Let an >0 and assume that bn = n+1 + B. What can we say about the convergence of an? an
With Proper explanation and example. Construct a context-free grammar for the language L={ ab”ab”a | n> 1}.
2. If S:= {1/n - 1/min, me N}, find inf S and sup S. 4. Let S be a nonempty bounded set in R. (a) Let a > 0, and let aS := {as : S ES). Prove that inf(as) = a infs, sup(as) = a sup S. (b) Let b <0 and let b = {bs : S € S}. Prove that inf(bs) = b supS, sup(bs) = b inf S. 6. Let X be a nonempty set and...
3. Let {Sn, n > 0} be a symmetric Random Walk on Z. Defined To inf(n > 1 : Sn-0} the time of first passage to state 0, prove that 2n - 1 for any n 2 1
2. (D5) Let n = o(a) and assume that a =bk. Prove that <a >=<b> if and only if n and k are relatively prime.
3. Let X N(20,1). What is P(X > 20) ? a) 0.25 b) 0.5 c) 0.75 d) 0.99