4. Consider the statement If Oscar eats Chinese food, then he drinks milk. (a) Write the...
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4. Consider the statement "If Oscar eats Chinese food, then he drinks milk." (a) Write the converse of the statement. (b) Write the contrapositive of the statement. (c) Is it possible for the contrapositive to be false? If it was, what would that tell you? (d) Suppose the original statement is true, and that Oscar drinks milk. Can you conclude anything (about his eating Chinese food)? Explain. (e) Suppose the original statement is true, and that Oscar does not drink milk. Can you conclude anything (about his eating Chinese food)? Explain. 7. Translate into symbols. Use E(x) for "x is even" and O(x) for "x is odd." (a) No number is both even and odd. (b) One more than any even number is an odd number. (c) There is prime number that is even. (d) Between any two numbers there is a third number. (e) There is no number between a number and one more than that number. 9. Suppose P(x) is some predicate for which the statement VxP(x) is true. Is it also the case that 3xP(x) is true? In other words, is the statement VxP(x)→ 3xP(x) always true? Is the converse always true? Explain. 10. For each of the statements below, give a domain of discourse for which the statement is true, and a domain for which the statement is false. (a) xy(y² = x). (b)x=y=(x< < y). (c) xyz(yz→ y ≤ x ≤z) Hint: domains need not be infinite. 4. Consider the statement "If Oscar eats Chinese food, then he drinks milk." (a) Write the converse of the statement. (b) Write the contrapositive of the statement. (c) Is it possible for the contrapositive to be false? If it was, what would that tell you? (d) Suppose the original statement is true, and that Oscar drinks milk. Can you conclude anything (about his eating Chinese food)? Explain. (e) Suppose the original statement is true, and that Oscar does not drink milk. Can you conclude anything (about his eating Chinese food)? Explain. 7. Translate into symbols. Use E(x) for "x is even" and O(x) for "x is odd." (a) No number is both even and odd. (b) One more than any even number is an odd number. (c) There is prime number that is even. (d) Between any two numbers there is a third number. (e) There is no number between a number and one more than that number. 9. Suppose P(x) is some predicate for which the statement VxP(x) is true. Is it also the case that 3xP(x) is true? In other words, is the statement VxP(x)→ 3xP(x) always true? Is the converse always true? Explain. 10. For each of the statements below, give a domain of discourse for which the statement is true, and a domain for which the statement is false. (a) xy(y² = x). (b)x=y=(x< < y). (c) xyz(yz→ y ≤ x ≤z) Hint: domains need not be infinite.
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4 a Converse If Oscar drinks milk then he eats Chinese food b Contrapositive If Oscar doesnt drink m... View the full answer
Related Book For
International Economics Theory and Policy
ISBN: 9780273754206
9th Edition
Authors: Paul R. Krugman, Maurice Obstfeld, Marc J. Melitz
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