1.5 Try it Out 2 Discrete Math

#82
by xOz11 - opened

๐Ÿ˜ƒ: Express the negation of the statement โˆ€xโˆƒy(xy = 1) so that no negation
precedes a quantifier. help me to solve this
๐Ÿค–: Sure! To express the negation of the statement โˆ€xโˆƒy(xy = 1), we can use the following formula:

ยฌ(โˆ€xโˆƒy(xy = 1))

In this formula, the negation operator ยฌ is used to indicate that the statement inside the parentheses is false. Since there are no quantifiers before the negation operator, the negation precedes the quantifier as you requested.

So, the entire formula can be read as "It is not the case that for every x, there exists y such that xy equals 1."
๐Ÿ˜ƒ: simplify that
๐Ÿค–: Certainly! Here's a simplified version of the formula:

ยฌโˆ€xโˆƒy(xy = 1)

I hope this helps! Let me know if you have any further questions or need additional assistance.

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