Math

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1.Suppose we are given logic statements p, q, and r.

a. If p → q and p → r, may we conclude that q → r? Answer yes or no and give a reason why.

b. What is the converse of the following: not p → not q

c. What is the contrapositive of r → q?

d. The statements p → q and q → r are given. If we know q is true, is p necessarily true? Explain.

  • Math -

    (a) No
    If it rains, I'll eat chicken.
    If it rains, I'll go outside.
    No way to conclude that eating chicken means going outside.

    (b) Come on. You know that the converse of p→q id q→p. So, ...

    (c) ~q → ~r

    (d) Nope. I'm sure you can come up with an example. (Use what you know about converses.)

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