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'.
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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∪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∩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.