Please answer the following questions in the attached image (Course: discrete structures and combination analysis) :

6. (4marks) Consider a relation R detined on positive integers, such that (x,y)R if and only it y is a prime number. Prove or disprove reflexivity, symmetry, antisymmetry and transitivity for h R={(x,4)x+y i prime } x+x=2x even x frime number cant be even Not refoncire. (y+x)= presine: Symmidrur. (3,2)R(2,3)R2=33+25Preme2+35Poino Not Anti \&ymindruc (x,y)&R&(y,z)R Prime Number: Even + Odd: So if x even, y add. 8 in (4,z);y odd,z even then (x,z)= even, eren, which x+z= prins Not transiture 7. (5 marks) Draw the Hasse diagram for the poset ({3,4,6,7,12,21,24,28,42},)