Suppose that a and b are sets with a 3 and b 5 both sets

Question

Discrete Math:

1. Suppose that A and B are sets with |A| = 3 and |B| = 5; both sets are drawn from a universe U with |U| = 11. Determine the possible values for each of the cardinalities below; give examples of the extreme (i.e. maximum and minimum) values.

(a) |A ∩ B|. 

1. Let S and T be (finite) sets. For each assertion below, determine whether it is true or false. If it's true, then explain why; if it's false, give an example to show that it's false.

(a) P(S ∪ T) = P(S) ∪ P(T). 

(b) If the sets A₁,A₂ partition S and the sets B₁,B₂ partition T, then the sets A₁×B₁, A₂ × B₁, A₁ × B₂, A₂ × B₂ partition S × T.