By Hogg R.V., McKean J.W., Craig A.T.

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**Extra info for Solution Manual for Introduction to Mathematical Statistics 6th Edition**

**Example text**

LB is true for 2. LB is false for 2. LB have the same truth-value in 2. 6. Let A and B be wffs such that vA = vB for each valuation v. Prove that both A -+ B and B -+ A are true wffs. 7. Let A and B be wffs such that both A vA = vB for each valuation v. 8. Given that A wff. -+ C and B -+ -+ B and B -+ A are true. Prove that C are true wffs, show that A V B -+ C is a true Use the Criterion for True Wffs to prove that none of the following wffs is true: 9. (Y). 10. Xv Y. 11. Y. 12. X-+ Y. 13. X-+ Y-'->-X 14.

Definition of Subwff. We say that B is a subwff of a wff A provided that B is a wff and there are expressions cp and 8 such that A = cpB8. So, a subwff of a wff A is a block of symbols contained in A that is itself a wff. (X))). In order to utilize our Fundamental Theorem about Wffs in this connection, we need to formulate the notion of a subwff in a manner that apes the definition of the notion of wff itself. Accordingly, we now introduce the concept of a component of a wff. Definition of Component.

Lemma 9. If I- C -+ A -+ B, then I- C -+ -,B -+ -,A. Dem. I- C -+ A -+ B is given, and I- A -+ B -+ -,B -+ -,A by Corollary 2; so I- C -+ ---,B -+ ---,A by Theorem 1, page 43. Exercises 1. Prove Lemma 1. 2. Show that A == B if 3. Let A and B be wffs such that A V C == B V C for some wff C. Is it necessarily the case that A == B? Justify your answer. 4. Let A and B be wffs such that A V C == B the case that A == B? Justify your answer. , provable wffs are equivalent). V C for each wff C. Is it necessarily 48 Chap.