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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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Some English adjectives are descriptive of themselves (for instance, the word polysyllabic is polysyllabic) whereas other are not monosyllabic). The word monosyllabic is not monosyllabic). The word monosyllabici refers to an monosyllabic). The word herterological refers to an adjective that does not describe itslf. Is heterological hererological? Exaplain your answer.

To determine

Some English adjectives are descriptive of themselves (for instance, the word polysyllabic is polysyllabic) whereas others are not (for instance, the word monosyllabic is not monosyllabic). The word heterological refers to an adjective that does not describe itself. Is heterological? Explain your answer.

Explanation

Given information:

Consider the following set of adjectives that do not describe themselves:

S={A|A is an adjective and AA}

Concept used:

Use Russell’s paradox which is stated, as follows:

If S={A|A is a set and AA} is the set of all sets that are not elements of themselves, then neither SS nor SS.

Calculation:

Consider the following set of adjectives that do not describe themselves:

S={A|A is an adjective and AA}

The objective is to check whether the adjective heterological is heterological or not.

Use Russell’s paradox which is stated, as follows:

If S={A|A is a set and AA} is the set of all sets that are not elements of themselves, then neither

SS nor SS

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