Question

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

Explanation:

Step1: Understand the meaning of \( B\cap C \)

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

Step2: Understand the meaning of \( \overline{B} \)

The complement \( \overline{B} \) represents the set of elements that are not in \( B \). So, we shade the region of the sample space \( S \) that is outside the circle \( B \).

Answer:

For part (a), shade the overlapping region of circles \( B \) and \( C \). For part (b), shade the region of \( S \) outside circle \( B \).