# Math

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“Vitamin E is a proven antioxidant and may help in fighting cancer and heart disease.” Is there anything ambiguous about this claim?

• Math -

Try to break up the statement into logical statements.

p=Vitamin E is a proven antioxidant
q=Vitamin E helps in fighting/preventing cancer
r=Vitamin E helps in fighting/preventing heart-disease.

The given statement is therefore equivalent to saying
p∧(q∨~q)∧(r∨~r)
where ~ represents negation, and if we interpret the "and" as a logical ∧.
Since the statement says "may help", it can go either way, so we have
(q∨~q) and (r∨~r), both of which are tautologies.

It is similar to saying "It may rain on New Year's Day". The statement is true whether it rains or not.

• Math -

"Vitamin E is a proven antioxidant and may help in fighting cancer and heart disease." Is there anything ambiguous about this claim?

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