Question

Consider A={x:x is an integer,0 < x ≤ 3}

(a) Write A in Roster form (1)

(b) Write the power set of A (1)

(c) The number of proper subsets of A=................. (1)​

Answer 1

Answer:

(a) A = {1, 2, 3}

(b) P(A) = {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

(c) 7

Step-by-step explanation:

A is a set of integers such that 0 < x ≤ 3. This means that it includes all integers from 1 to 3 but not 0. So, in Roster form, A is written as {1, 2, 3}.

                                              (a)  A = {1, 2, 3}

The power set of A is the set of all subsets of A, including the empty set (∅) and A itself. In this case, there are 3 elements in A (1, 2, 3), so there are (2³ = 8) possible subsets of A. These subsets are ∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, and {1, 2, 3}.

                    (b) P(A) = {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

The number of proper subsets of A is the number of subsets of A that do not include A itself. There are (2³ = 8) possible subsets of A. This is because there are 8 possible subsets of A in total, but 1 of them is A itself. So, the number of proper subsets is 8 - 1 = 7.

                                                        (c) 7

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Answer 2

Answer:

The correct answer would be, (a) A = {1, 2, 3}, (b) P(A) = {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}, (c) 7, from subsets.

Step-by-step explanation:

A is a collection of numbers such that 0 x 3 = 1. That is, it covers all numbers from 1 to 3 but not 0. So, A is written as 1, 2, 3 in Roster form.

(a) A = {1, 2, 3}

The set of all subsets of A, including the empty set () and A itself, is the power set of A. Because A has three components (1, 2, 3), there are (23 = 8) potential subsets of A. These subsets are, 1, 2, 3, 1, 2, 3 and 1, 2, 3 respectively.

(b) P(A) = {∅, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}}

The number of correct A subsets is the number of A subsets that do not include A itself. A may be divided into (23 = 8) subgroups. This is due to the fact that there are 8 potential subsets of A, but only one of them is A itself. So there are 8 - 1 = 7 appropriate subsets.

(c) 7

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