How To Instal Themes On S2?

Given that S1={ 1,2,3,4,5,6} and S2= {1,2,3,4,5,6}. let S = S1 x S2 denote the set of all ordered pairs.?

• Given that S1={ 1,2,3,4,5,6} and S2= {1,2,3,4,5,6}. let S = S1 x S2 denote the set of all ordered pairs. Define the following subsets of S: A={(s1, s2) l s1 Є S1 and s2 Є S2, s2 is even} B={(s1, s2 ) l s1 Є S1 and s2 Є S2, s1 +s2 is even} C={(s1, s2 ) l s1 Є S1 and s2 Є S2, at least one numberin the pair is odd} List the elements in 1.A 2.B 3.C 4.C' 5. A ∩ B 6. A ∩ B' 7. A' U B 8. A' ∩ C 9.Describe in words the members of A' and A ∩ B.

• Answer:

  1) A={(s1, s2) l s1 Є S1 and s2 Є S2, s2 is even} A={(1,2),(2,2),(3,2),(4,2),(5,2),(6,2)… 2) B={(s1, s2 ) l s1 Є S1 and s2 Є S2, s1 +s2 is even} B={(1,1),(1,3),(1,5),(2,2),(2,4),(2,6)… 3) C={(s1, s2 ) l s1 Є S1 and s2 Є S2, at least one number in the pair is odd} C={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)… 4) C'={(2,2),(2,4),(2,6),(4,2),(4,4),(4,6),… 5) A ∩ B = {(2,2),(4,2),(6,),(2,4),(4,4),(6,4),(2,6… 6) A ∩ B' = {(1,2),(3,2),(5,2),(1,4),(3,4),(5,4),(1,… 7) A' U B = {((1,1),(1,3),(1,5),(3,1),(3,3),(3,5),(5… 8) A' ∩ C = {(1,1),(1,3),(1,5),(2,1),(2,3),(2,5),(3,… 9) A' = the set of ordered pairs (s1,s2) where s2 is odd. 10) A ∩ B = the set of ordered pairs (s1,s2) where s1+s2 is even and s2 is even (=> s1 and s2 are even)