The event 'A or B' corresponds to the union of sets A and B, denoted as A B. This set includes all elements that are in A, or in B, or in both, without repetition.

The event 'A and B' corresponds to the intersection of sets A and B, denoted as A B. This set includes only the elements that are common to both A and B.

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'.

Answer: (i) $A \cup B = \{1, 2, 3, 5\}$ (ii) $A \cap B = \{3, 5\}$ (iii) $A - B = \{2\}$ (iv) $A' = \{1, 4, 6\}$

Step-by-step solution

Step 1: Define the Sample Space and Events

First, we define the sample space $S$ for rolling a die, which includes all possible outcomes from 1 to 6. Then, we identify the elements for event A, 'getting a prime number', which are numbers greater than 1 divisible only by 1 and themselves. Finally, we identify the elements for event B, 'getting an odd number'.

Step 2: Calculate A or B

The event 'A or B' corresponds to the union of sets A and B, denoted as $A \cup B$ . This set includes all elements that are in A, or in B, or in both, without repetition.

Step 3: Calculate A and B

The event 'A and B' corresponds to the intersection of sets A and B, denoted as $A \cap B$ . This set includes only the elements that are common to both A and B.

Step 4: Calculate A but not B

The event 'A but not B' corresponds to the set difference $A - B$ . This set includes all elements that are in A but are not in B.

Step 5: Calculate not A

The event 'not A' corresponds to the complement of set A, denoted as $A'$ . This set includes all elements in the sample space $S$ that are not in A.

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