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

<p></p><br /><p>1. The given question pertains to the field of logic, specifically quantifiers in predicate logic.</p><br /><p>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."</p><br /><p>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."</p><br /><p>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."</p><br /><p>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.</p>