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question 3 (1 point) if ee y aa xp(x,y) is a true proposition then aa x ee yp(x,y) is always true. true false

Question

Question 3 (1 point) If EE y AA xP(x,y) is a true proposition then AA x EE yP(x,y) is always true. True False

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Answer

False

Explanation

1. The given question pertains to the field of logic, specifically quantifiers in predicate logic.2. The statement "∃y ∀x P(x, y)" means "There exists a 'y' such that for all 'x', the proposition P(x, y) is true."3. The statement "∀x ∃y P(x, y)" means "For all 'x', there exists a 'y' such that the proposition P(x, y) is true."4. To understand the difference, consider an analogy: The first statement is like saying "There is a single book that everyone has read." The second statement is like saying "Everyone has read at least one book, but it might not be the same book for everyone."5. It is clear from the analogy that the truth of the first statement does not necessarily imply the truth of the second statement. Therefore, the assertion that if "∃y ∀x P(x, y)" is true then "∀x ∃y P(x, y)" is always true, is false.