Critical Thinking PHL 2020 Homework 3
I. Symbolize the following claims, using the letters indicated.
P = We plant perennials; A = We plant annuals; S = We plant from seed; C = We plant from cuttings.
If we plant both annuals and perennials, then we can plant from both seed and cuttings.
We cannot plant perennials if we plant from either seed or from cuttings.
If we don’t plant from seed, then we can’t plant either annuals or perennials.
The only way we can plant both annuals and perennials is by planting from both cuttings and seed.
Either we will plant from cuttings, or, if we don’t plant perennials, we can plant from seed.
II. Use the regular truth-table method to determine whether these are valid or invalid.
A v B/~A ( ~C//C ( B
2. ~A((B &~C) /(B&~C) ((A v B)//~A((A v B)
III. Use the short truth-table method to determine whether these are valid or invalid.
1. A ( B/B ( C/C ( D/A//D v E
2. ~E v ~D/~(A ( C)/~(~B v ~E)/~(A & B) v (C ( D)// ~A
IV. Using rules construct deductions to prove that the following are valid.
1. 1.~(A v B)
2. 1.A v ~B
2.C ( B
/( C( A
3. 1.(A ( B) & (C ( D)
2.B ( ~D
3.~E ( (A & C)
A ( (B & C)
~D ( ~(B v C)
/( A ( D
A ( (B & C)
C ( (D v E)
/( ~(~A v D) ( E
V. Determine whether the following symbolized arguments are valid or invalid. For any that are valid, construct a deduction.
A v (C & ~D)
B ( ~A
/ B ( D
(A ( D) & C
2. C ((D ( B)
VI. Use Conditional Proof to construct new deduction.
1. (G v H) ( (S & T)
2. (T v U) ( (C & D)
/ G ( C
VII. Symbolize the following arguments, and test them for validity. For those that are valid, construct a deduction.
If government deficits continue at their present rate and a recession sets in, then interest on the national debt will become unbearable and the government will default on its loans. If a recession sets in, then the government will not default on its loans. Therefore, either government deficits will not continue at their present rate or a recession will not set in. (C, R, I, D)
If a superconducting particle collider is built, then the data it could yield would benefit scientists of all nations and it deserves international funding. Either a superconducting particle collider will be built, or the ultimate nature of matter will remain hidden and the data it could yield would benefit scientists of all nations. Therefore, the data a superconducting particle collider could yield would benefit scientists of all nations. (S, D, I, U)