Question

in the venn diagram below, a and d are events in the sample space s. (note: for any event x, we use \\(\overline{x}\\) to denote
ot x.\) (a) shade a ∩ d. (b) shade a ∪ d.

Explanation:

Step1: Recall intersection definition

The intersection \(A\cap D\) is the set of elements that are in both \(A\) and \(D\). So we shade the overlapping region of circles \(A\) and \(D\).

Step2: Recall union definition

The union \(A\cup D\) is the set of elements that are in either \(A\) or \(D\) or both. So we shade the entire area covered by circle \(A\) and circle \(D\) including the overlapping part.

Answer:

(a) Shade the overlapping part of circles \(A\) and \(D\).
(b) Shade the entire area covered by circle \(A\) and circle \(D\) (including the overlapping part).