Let S be the set of outcomes when two distinguishable dice are rolled, let E be the subset of outcomes in which at least one die shows an even number, and let F be the subset of outcomes in which at least one die shows an odd number. List the elements in the given subset.

Step-by-step explanation:

given that S be the set of outcomes when two distinguishable dice are rolled, let E be the subset of outcomes in which at least one die shows an even number, and let F be the subset of outcomes in which at least one die shows an odd number

E = atleast one shows even number

i. e. both cannot show odd number

So elements of E are

E = { (1,2) (1,4) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,2) (3,4) (3,6) (4,1) (4,2) (4,3) (4,4 (4,5) (4,6),5,2) (5,4) (5,6) (6,1) (6,2) (6,3) (6,4 (6,5) (6,6) }

F = atleast one die shows odd

F={ (1,1) (1,2) (1,3), (1,4) (1,5) (1,6) (2,1) (2,3) (2,5) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,3) (4,5) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,3) ((6,5) }