Question

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

Explanation:

Step1: Understand the meaning of intersection

The intersection \(A\cap C\) represents the elements that are in both \(A\) and \(C\). So, we shade the overlapping region of the two circles.

Step2: Understand the meaning of union

The union \(A\cup C\) represents the elements that are in \(A\) or \(C\) or both. So, we shade all the regions covered by either circle \(A\) or circle \(C\) (including the overlapping part).

Answer:

For part (a), shade the overlapping region of circles \(A\) and \(C\). For part (b), shade all of circle \(A\) and all of circle \(C\) (including their overlap).