If A and B are mutually exclusive events. Their relation will be:

The correct answer is A ∩ B = φ. This notation states that the intersection of events A and B is the empty set, which perfectly describes mutual exclusivity.

Step-by-Step Explanation

• Step 1 – Define mutually exclusive events:
  
  Two events are mutually exclusive if they cannot occur simultaneously. For example, when rolling a die, getting a "2" and getting a "5" on the same single roll are mutually exclusive; both outcomes cannot happen at once.
• Step 2 – Understand the set notation:
  
  In probability, events are represented as sets of outcomes.
  
  A ∩ B (A intersection B) is the set of outcomes that belong to both A and B.
  
  φ (the Greek letter phi) denotes the empty set, meaning there are no elements.
• Step 3 – Apply the definition:
  
  For mutually exclusive events, there is no common outcome. Therefore, the set containing outcomes common to both A and B is empty.
  
  This is written as: A ∩ B = φ
• Step 4 – Eliminate incorrect options:
  
  A ∩ B = S: This would mean the intersection is the entire sample space, implying A and B always happen together (the exact opposite of mutual exclusivity).
  
  A ∪ B = φ: This would mean that neither A nor B ever happens, which is impossible for valid events.
  
  A = B: If A and B are the same event, they always occur together, again contradicting mutual exclusivity.
• Step 5 – Probability consequence:
  
  For mutually exclusive events, P(A ∩ B) = 0, and the addition rule simplifies to P(A ∪ B) = P(A) + P(B).

Therefore, the correct relation for mutually exclusive events A and B is A ∩ B = φ.