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Chapter 3: Problem 34

Find four proper subsets of \(\mathrm{P}=\\{\mathrm{n}: \mathrm{n} \in \mathrm{I},-5<\mathrm{n} \leq 5\\}\).

Short Answer

Expert verified
Four proper subsets of the set \(P=\{-4, -3, -2, -1, 0, 1, 2, 3, 4, 5\}\) are: 1. \(A = \{-4, -3, -2, -1\}\) 2. \(B = \{0, 1, 2, 3, 4, 5\}\) 3. \(C = \{-4, -2, 0, 2, 4\}\) 4. \(D = \{-3, -1, 1, 3, 5\}\)

Step by step solution

01

Find the elements in the set P

Given that \(P=\{n: n \in \text{I}, -5<n\leq5\}\), we are looking for integer values between -5 and 5, but not including -5 since it's a strict inequality. So the set P must be: \[P=\{-4, -3, -2, -1, 0, 1, 2, 3, 4, 5\}\]
02

Determine four proper subsets of the set P

Now, select four proper subsets from the set P. A proper subset is a set that contains some elements of the original set but not all of them. Here are four examples: 1. \(A = \{-4, -3, -2, -1\}\) (Only including the negative elements.) 2. \(B = \{0, 1, 2, 3, 4, 5\}\) (Only including the non-negative elements.) 3. \(C = \{-4, -2, 0, 2, 4\}\) (Only including the even elements.) 4. \(D = \{-3, -1, 1, 3, 5\}\) (Only including the odd elements.) These four sets (A, B, C, and D), are proper subsets of the set P, as they each contain some elements of P, but not all of them.

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