Question

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 foodxplain. Suppose the original statement is true, and that Oscar does not drink milk. Can you conclude anything (about his eating Chinese food)? Explain e.

Answer 1

Answer:

From the given problem statement,the converse of the statement is given below

If he drinks milk then Oscar eats Chinese food.

Answer 2

Step-by-step explanation:

Consider the provided statement.

"If Oscar eats Chinese food, then he drinks milk."

Here p is Oscar eats Chines food and q is he drinks milk.

Converse is interchange the two statement.

Converse: "If Oscar drinks milk, then he eats Chinese food"

Contrapositive is negative both statement and interchanges them.

Part (b) Contrapositive: "If Oscar doesn't drink milk, then he doesn't eat Chinese food"

Part ( c) If the provided statement is true, then the contrapositive is always true because contrapositive is logically equivalent to the provided statement. If provided statement is false, then the contrapositive is always false.

Part (d) let the original statement is true, and we know that Oscar drinks milk, then we still would not be able to make any conclusion about his Chinese food eating habits.

Because the statement is true if "Oscar eats Chinese food" is true Oscar may or may not eat chines food.

The above converse may be false.

Part (e) Suppose the original statement is true, and that Oscar does not drink milk. It means Oscar doesn't eat Chinese food. Because if Oscar eats Chinese food, then according to the truth of the original statement "Oscar drinks milk" to be true which is the contradiction.

Thus, Oscar doesn't eat Chinese food.