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## mathematical notation

Write the following is mathematical notation
a) All cats are friendly
b) Some horses are unrideable

I assume you are asking for the logical equivalents of these statements in predicate calculus.

a.)  ∀x(if x is a cat then x is friendly)
b.)  ∃x(x is a horse and x is unrideable)

As per part b, note that the modifier "some" equates to "at least one" in predicate calculus.  There may be more than one unrideable horse, but the "some" statement is true if there is at least one at a minimum.

If more information was known, more exact statements of the "some" modifier could be made using the language of statistics;  that is "The probability that a horse is unrideable is 30%" might be a more precise restatement of "some".  However, there is not sufficient information in this problem to make such a statement, and the problem calls for a statement in the Predicate Calculus.
Hi Daniel;
Do you need one or two mathematical notations?

cats=friendly

horses(x)=un-ride-able
x=percentage represented as a decimal (e.g., 40% expressed as 0.40).