Draw a Venn diagram that represents (S ∪ T) − (S ∩ T).

Sketch the corresponding venn diagram:

Describe the set {x € R? : doo(T, (0,0)) = 1}.

Consider the following set of ordered pairs of the elements of a set A = {1, 2, 3,4} of numbers and a set B = {a, b, c, d} of letters. {(1, d), (2, d) , (3, a), (2, c), (4, b)} Select all options true of this set. This is not a map from A to B. This is a map from A to B and is onto. This is a map from A to B and is one-to-one. This is a map from A to B and is neither one-to-one nor onto. Map Properties II Consider the following set of ordered pairs of the elements of a set A = {1, 2, 3, 4} of numbers and a set B = {a, b, c, d} of letters. {(1, a), (2, b) , (3, a) , (4, d)} Select all options true of this set. This is not a map from A to B. This is a map from A to B and is onto. This is a map from A to B and is one-to-one. This is a map from A to B and is neither one-to-one nor onto.

Find two sets A and B such that A E B and AB.

Consider following five sets: I. { , } { } II. { } III. IV. { , , } V. { , } Find all linearly independent set(s). (a) I (b) I and IV (c) I and II (d) II, IV and V (e) II (f) II

Draw a Venn diagram for the symmetric difference of the sets A and B.

Let A E R2x3, be R². Determine whether or not S = {x € R³ | Ax = b, x₁ ≤ 0, x₂ ≤ 0} X2 is a convex set.

Exercise 3.3.15. Prove or find a counterexample to the following statement. Let A, B and C be sets. Then (A-B) UC = (AUBUC) - (ANB).

Prove: bd (s) = 5 TR-S bd (s) is a closed set