Question

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 1

@oldrin.bataku

Answer 2

First consider our possibilities (i.e. our universe) for a dice roll.$$\{1,2,3,4,5,6\}$$Now, consider the results that correspond to event \(A\), i.e. which numbers are prime:$$A=\{2,3,5\}$$Similarly, consider whose which correspond to event \(B\), i.e. are odd:$$B=\{1,3,5\}$$
Can you determine \(A\cup B, A\cap B, A\backslash B,A^c\)?

Answer 3

ok

Answer 4

$$A\cup B=\{1,2,3,5\}\\A\cap B=\{3,5\}\\A\backslash B=\{2\}\\A^c=\{1,4,6\}$$

Answer 5

ok

Answer 6

Intuitively, the union of the sets is the possible values that are prime, odd, or both. Similarly, the intersection is precisely only those that are both prime and odd. The difference of A and B is the elements of A that are not in B, i.e. the prime numbers that are not odd. The complement of A, i.e. the elements that are not in A, are those that are not prime.

Answer 7

ok

Answer 8

Thank you sir