For the following statements about sets: prove if true, give counterexample if false. Use only the...

Transcribed Image Text:

For the following statements about sets: prove if true, give counterexample if false. Use only the definitions of the set operators; do not use any derived properties or Venn diagrams. Hint: prove statements in (a) the forwards direction. direction; (b) the backwards 1. For all sets X and Y, X C Y if and only if X - Y is the empty set. 2. For all sets X and Y, XUY = X ^Y if and only if X = Y. Hint: look at the notes' definition of set equality. 3. For all sets X and Y, X C Y if and only if X - Y is the empty set. For the following statements about sets: prove if true, give counterexample if false. Use only the definitions of the set operators; do not use any derived properties or Venn diagrams. Hint: prove statements in (a) the forwards direction. direction; (b) the backwards 1. For all sets X and Y, X C Y if and only if X - Y is the empty set. 2. For all sets X and Y, XUY = X ^Y if and only if X = Y. Hint: look at the notes' definition of set equality. 3. For all sets X and Y, X C Y if and only if X - Y is the empty set.

Answer rating: 100% (QA)

Answer Lets analyze each statement one by one 1 For all sets X and Y XY if and only if XY is the empty set a Forwards Direction Assume XY This means t... View the full answer