Mathematics question:SETS?

Question

Find sets when possible satsfying each of the following conditions:

a. # of elements in A plus # of elements in B is greater than # of elements in A U B. ***U represents Union

b. # of elements in I plus # of elements in J is less than # of elements in I U J.

c. # of elements in E plus # of elements in F equals # of elements in E U F.

d. # of elements in G plus number of elements in K equals number of elements in G (upside down U sign respresenting Intersection) K.

HELP!!

Answer 1

a. # of elements in A plus # of elements in B is greater than # of elements in A U B.

If A and B are not disjoint, then the elements in A ∩ B are counted twice for {# of elements in A} plus {# of elements in B} but are only counted once when you count the elements of A U B directly.

Example: A = {1,2,3} and B = {2,3,4}.

Then {# of elements in A} plus {# of elements in B} = 3 + 3 = 6
But {# of elements in A U B} = 4.

b. # of elements in I plus # of elements in J is less than # of elements in I U J.

Not possible.

c. # of elements in E plus # of elements in F equals # of elements in E U F.

True if the sets are disjoint.

Example: E = {1,2,3} and F = {4,5,6}.

Then {# of elements in E} plus {# of elements in F} = 3 + 3 = 6
And {# of elements in E U F} = 6 also.

d. # of elements in G plus number of elements in K equals number of elements in G ∩ K.

True if both G and K are the empty set.

Example: G = Ø and K = Ø

Then {# of elements in G} plus {# of elements in K} = 0 + 0 = 0
And {# of elements in G ∩ K} = 0 also.

Answer 2

a) Let A be a set of integers ranges from 1-10 (i.e. 0
For answers to questions b to d you can contact me.

Answer 3

(a), (b), (c): Not possible, 'coz n(X) + n(Y) (d): Not possible, 'coz n(X) + n(Y) >or= n(X intersection Y)