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brilliants [131]
3 years ago
12

Write down the negation of each statement

Mathematics
1 answer:
prohojiy [21]3 years ago
6 0

Answer:

1. ∀ y ∈ Z such that ∃ x ∈ Z, ¬R (x + y)

2. ∃ x ∈ Z, ∀ y ∈ Z such that ¬R(x + y)

Step-by-step explanation:

If we negate a quantified statement, first we negate all the quantifiers in the statement from left to right, ( keeping the same order ) then we negative the statement,

Here, the given statement,

1. ∃y ∈Z such that ∀x ∈Z, R (x + y)

By the above definition,

Negation of this statement is ∀ y ∈ Z such that ∃ x ∈ Z, ¬R (x + y),

2. Similarly,

The negation of statement ∀x ∈Z, ∃y∈Z such that R(x + y),

∃ x ∈ Z, ∀ y ∈ Z such that ¬R(x + y)

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<h3>What is combination?</h3>

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter. In combinations, you can select the items in any order. Combinations can be confused with permutations.

Given:

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