Answer :
(i) To list the members of the set P, where P is defined as the set of all prime numbers less than 10, we need to first identify which numbers below 10 are prime. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
The prime numbers less than 10 are:
- 2 (the only even prime number)
- 3
- 5
- 7
Therefore, the set P = {2, 3, 5, 7}.
(ii) To find the number of subsets of P, we use the formula related to the number of subsets a set can have. If a set has n elements, then the number of subsets it can have is 2^n. The set P has 4 members, so the number of subsets of P is 2^4.
Therefore, the number of subsets of P = 2^4 = 16.
(iii) Subsets of P containing just one member are simply the individual members of P themselves. Each of these subsets will contain exactly one of the prime numbers from P.
The subsets containing one member are:
- {2}
- {3}
- {5}
- {7}
These are all the subsets that include exactly one member of the set P.
The prime numbers less than 10 are:
- 2 (the only even prime number)
- 3
- 5
- 7
Therefore, the set P = {2, 3, 5, 7}.
(ii) To find the number of subsets of P, we use the formula related to the number of subsets a set can have. If a set has n elements, then the number of subsets it can have is 2^n. The set P has 4 members, so the number of subsets of P is 2^4.
Therefore, the number of subsets of P = 2^4 = 16.
(iii) Subsets of P containing just one member are simply the individual members of P themselves. Each of these subsets will contain exactly one of the prime numbers from P.
The subsets containing one member are:
- {2}
- {3}
- {5}
- {7}
These are all the subsets that include exactly one member of the set P.
