Rewrite each of the following statements in the form "∀ x, ." (a) All dinosaurs are extinct. ∀ x, . (b) Every real number is positive, negative, or zero. ∀ x, . (c) No irrational numbers are integers. ∀ x, .(d) No logicians are lazy. ∀ x, .(e) The number 2,147,581,953 is not equal to the square of any integer. ∀ x, .(f) The number −1 is not equal to the square of any real number.

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Step-by-step explanation:

Essentially, we have to replace "quantifier words" like "All", "Every" by the universal quantifier ∀.

a) ∀ dinosaur x, x is extinct.

b) ∀ real number x, x is positive, negative, or zero.

c) ∀ irrational number x, x is not an integer.

d) ∀ logician x, x is not lazy.

e) ∀ integer x, x²≠ 2,147,581,953.

f)  ∀ real number x, x²≠ -1.

In a) and b) we replace the words without major changes. In the other statements, we modify the statement using negation. For example, "No irrational numbers are integers." is equivalent to "Every irrational number is not integer".

this is not the answer this is just a question. is this middle school math?

step-by-step explanation:

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: