Mathematics
Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Write the subset of A containing :
(i) all odd numbers
(ii) all prime numbers
(iii) all multiples of 4.
Answer
(i) all odd numbers
Given A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.
Odd numbers are: {1, 3, 5, 7, 9, 11}
(ii) all prime numbers
Prime numbers are natural numbers greater than 1 that have exactly two factors: 1 and the number itself. From set A, these are 2, 3, 5, 7, and 11.
All prime numbers are: {2, 3, 5, 7, 11}
(iii) all multiples of 4.
Multiples of 4 are numbers that can be divided by 4 without a remainder. Within the range of set A, these are 4 x 1, 4 x 2, and 4 x 3.
All multiples of 4 are: {4, 8, 12}
Related Questions
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Which of the following statements are true ?
(i) {a} ⊂ {a, b, c}
(ii) {a} ⊂ {b, c, d, e}
(iii) Φ ⊂ {a, b, c}
(iv) Φ ∈ {a, b, c}
(v) 0 ∉ Φ
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(viii) Every subset of an infinite set is infinite.
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(ii) B'
(iii) C'
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