Question

Write the cardinal number of p intersection Q if p and Q are disjoint sets.​

Answer 1

P(p∩Q) = 0.

Explanation:

Given the Addition Rule:

P(p∪Q) = P(p) + P(Q) - P(p∩Q)

P(p or Q) = P(p) + P(Q) - P(p and Q)

Events p and Q are disjoint (or mutually exclusive) if they cannot occur at the same time. (That is, disjoint events do not overlap.)

Hence, whenever p and Q are disjoint, P(p and Q) becomes zero in the formal addition rule, so for disjoint events p and Q we have:

P(p or Q) = P(p) + P(Q).

Therefore, the cardinal number of P(p∩Q) = 0.