Write ⊆ or ⊄ in the space provided.

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Discussion Overview

The discussion revolves around determining whether certain mathematical sets and intervals are subsets or not, specifically using the symbols ⊆ (subset) and ⊄ (not a subset). The scope includes mathematical reasoning and set theory concepts.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • Some participants agree that for the intervals (3,5) and [3,5], the first two are correctly identified as subsets.
  • One participant questions the interpretation of the notation for the fourth item, suggesting that the notation N * Z and Z * N may refer to Cartesian products of sets.
  • Another participant notes that P(∅) equals {∅}, which is relevant to the third item in the list.
  • There is acknowledgment of a mistake regarding the third item, with one participant admitting to slipping on that point.

Areas of Agreement / Disagreement

Participants generally agree on the correctness of the first two items, but there is uncertainty regarding the third and fourth items, with multiple interpretations and no consensus reached on those.

Contextual Notes

There are unresolved assumptions regarding the notation used for the Cartesian products and the implications of the intervals on the real line.

KOO
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Write ⊆ or ⊄ in the space provided.

(3,5) _____ [3,5]
[-1,4] ____ (-1,4)
{∅} _____ P(∅)
N * Z ____ Z * NMy Solution)

⊆
⊄
⊄
⊆
 
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KOO said:
Write ⊆ or ⊄ in the space provided.

(3,5) _____ [3,5]
[-1,4] ____ (-1,4)
{∅} _____ P(∅)
N * Z ____ Z * NMy Solution)

⊆
⊄
⊄
⊆

Hi KOO! :)

The first 2 are correct.

Edit: see Evgeny.Makarov's post for the 3rd.

As for the 4th, can I assume you intended $\mathbb N \times \mathbb Z \underline{\qquad} \mathbb Z \times \mathbb N$?
If so then the left hand side has elements like (1,1) and (1,-1), while the right hand side has elements like (-1,1) and (1,1)...
 
I assume the first two questions are about intervals on the real line. Then I agree.

KOO said:
{∅} _____ P(∅)
Note that P(∅) = {∅}.
 
Evgeny.Makarov said:
Note that P(∅) = {∅}.

Good point.
Slipped on that one.
 

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