A. Directions. 1. Translate the following argument into symbolic notation using the translation dictionary provided at the end of this paragraph. 2. Prove that the
argument is valid using the method of Natural Deduction as outlined in
Chapter 7 of Hurley's A Concise Introduction to Logic, 12th edition. Do not use Conditional Proof (CP) in this proof. [Trans. Dict.: E= kangaroos will be saved from extinction; H = Australian hunters will cease killing millions of kangaroos yearly; M = sports shoe manufacturers decline to use kangaroo hides in their products]

B. Directions. Prove the following three (3) arguments to be valid using
the method of Natural Deduction. Do not use Rule of Conditional Proof in these proofs.
B.1.
1. [(B ->E) -> G]
2. (G - > ~ G) / B

B.2.
1. ~ (D -> R) / ~(R & P)

B.3.
1. - W
2. [S -> ( ~S v W) / ~S

Part A:
If sports shoe manufacturers decline to use kangaroo hides in their products, then Australian hunters will cease killing millions of kangaroos yearly. It is false that both Australian hunters will cease killing millions of kangaroos yearly and that the kangaroo will not be saved from extinction. Hence, if sports shoe manufacturers decline to use kangaroo hides in their products,then th kangaroo will be saved for extinction.

C. Directions. Show the following two (2) arguments to be valid using Conditional Proof in the method of Natural Deduction, as Hurley outlines it in Chapter 7.

C.1.
1. [~(Nv~A) -> ~ X]
2. [A -> (N -> C)] / [X - >(A -> - C)]

C.2.
1. [J -> (T & L)]
2. [P-> (R & M) / [(L - > P) -> (J - > M)]

A. Directions. 1. Translate the following argument into symbolic no...