or B’ Recall that union of two sets A and B denoted by A ∪ B contains all those elements which are either in A or in B or in both. When the sets A and B are two events associated with a sample space, then ‘A ∪ B’ is the event ‘either A or B or both’. This event ‘A ∪ B’ is also called ‘A or B’. Therefore Event ‘A or B’ = A ∪ B = { ω : ω ∈ A or ω ∈ B} .
The Event ‘A and B’ We know that intersection of two sets A ∩ B is the set of those elements which are common to both A and B. i.e., which belong to both ‘A and B’. If A and B are two events, then the set A ∩ B denotes the event ‘A and B’. Thus, A ∩ B = { ω : ω ∈ A and ω ∈ B} For example, in the experiment of ‘throwing a die twice’ Let A be the event ‘score on the first throw is six’ and B is the event ‘sum of two scores is atleast ’ then A = {( , ), ( , ), ( , ), ( , ), ( , ), ( , )}, and B = {( , ), ( , ), ( , )} so A ∩ B = {( , ), ( , )} Note that the set A ∩ B = {( , ), ( , )} may represent the event ‘the score on the first throw is six and the sum of the scores is atleast ’.
. The Event ‘A but not B’ We know that A–B is the set of all those elements which are in A but not in B. Therefore, the set A–B may denote the event ‘A but not B’.We know that A – B = A ∩ B´ Example Consider the experiment of rolling a die. Let A be the event ‘getting a prime number’, B be the event ‘getting an odd number’.
Write the sets representing the events (i) Aor B (ii) A and B (iii) A but not B (iv) ‘not A’. Solution Here S = { , , , ,