PLEASE answer each question with a true or false!
True-false questions
)The coefficient of x7y4 in (2x - 3y)11 is equal to 2734(l4) 2. If A is the set {1,2,3,4,5,6}, then A has 20 subsets that each have exactly 2 elements. 3.For any a,b e Z,if there exist x,y E Z such that ax+by=4,then GCDa,b=4 4. The numbers 12344 and 24689 are relatively prime 5. For all a,b,c E Z,if ac and b|c, then ab|c. 6.Let A={1,2,3},and let R={,1,/,21,,233/,33}.Then R is an equivalence relation on A.
If A={1,2,3,4} and P={{1,3},{2},{4}}, then there is an equivalence relation on A whose equivalence classes are precisely the elements of P.
8. For any set A, every relation on A that is symmetric and transitive must be an equivalence relation.
One transversal for the equivalence relation "congruence modulo 6" on Z is the set {7, 14,21,28, 35,42}.
10. Let A be a set and let ~ be an equivalence relation on A. For any element x e A,denote the equivalence class of x by []. Let a, b e A be arbitrary, and suppose that [a] [b]. Then a~b.
