Please solve, discrete structures

4. (4 marhs) Prove or disprove rellesivily, symgetry, ansisytnmetry and transativisy fat a relation: defined on the set of all non-emply strings mache up of letrers from the finglish anphabet, suchi that string s1 is in relation with spifs s2 if and only of the last lester in s1. conncise with the first fether in $2 5. (7 marks) Below is the matrix representation of a partial ordering on the set {a,b,c,d,e,f,g,h} : 1000000001000000001000001111000011111000111101001111011011110111 a) Draw the Hasse diagram of the poset. b) What are the minimal elements? Is there a least element? c) What are the maximal elements? Is there a greatest element? d) What are the upper bounds of {a,d,e} ? Is there a least upper bound? e) What are the lower bounds of {d,f} ? is there a greatest lower bound? f) Find a subset of {a,b,c,d,e,f,g,h} with 4 elements that does not have any upper bound or lower bound