Answer:
<h3>For two events A and B show that P (A∩B) ≥ P (A)+P (B)−1.</h3>By De morgan's law
which is Bonferroni’s inequality
<h3>Result 1: P (Ac) = 1 − P(A)</h3>Proof
If S is universal set then
Proof:
If S is a universal set then:
Which show A∪B can be expressed as union of two disjoint sets.
If A and (B∩Ac) are two disjoint sets then
B can be expressed as:
If B is intersection of two disjoint sets then
Then (1) becomes
Proof:
If A and B are two disjoint sets then
Proof:
If B is subset of A then all elements of B lie in A so A ∩ B =B
where A and A ∩ Bc are disjoint.
From axiom P(E)≥0
Therefore,
P(A)≥P(B)