Question

Use natural deduction to derive the conclusion in each problem.

Use conditional proof or indirect proof as needed:

1. | (x)(Jx⊃∼Ga) | |

2. | (∃x)(Jx • Gc) | / a ≠ c |

Answer #1

INSTRUCTIONS: Use natural deduction to derive
the conclusion in each problem.
Use conditional proof or indirect proof as needed:
1.
(x)[(Kx∨Nx)⊃(Ex •∼Rx)]
2.
(x)[(Kx∨Sx)⊃(Rx∨Hx)]
/ (x)[Kx⊃(Ex • Hx)]

5) Translate the following argument into symbolic form and then
use natural deduction (first 18 rules of inference) to derive the
conclusion of each argument. Do not use conditional proof or
indirect proof.
The Central Intelligence Agency (CIA) will lose its funding only
if the President thinks that it is wise and the Congress supports
the move. If either Congress supports the move or covert operations
run amok, then the CIA will have political problems. Therefore, if
the CIA will...

1)Translate all the definitions needed to derive the conclusion
into propositional formulas (i.e., premises)
2)Derive your proof for S using natural deduction with the
premises.
S: there exist irrational numbers a and b such that a^b is
rational
A: √2 is rational

1)Translate all the definitions needed to derive the conclusion
into propositional formulas (i.e., premises)
2)Derive your proof for S using natural deduction with the
premises.
S: there exist irrational numbers a and b such that a^b is
rational
A: √2 is rational
B: √2^√2 is rational
C: √2^√2*√2 is rational

Consider the natural deduction proof given below. Using your
knowledge of the natural deduction proof method and the options
provided in the drop-down menus, fill in the blanks to identify the
missing information (premises, inferences, or justifications) that
completes the given application of the simplification (Simp)
rule.
1.(M ≡ O) • ~(S ⋁ G)
2.M
3.~(S ⋁ G) • (O ⊃ ~M)
4.~S/ ~(S ⋁ G)
5.~(S ⋁ G) _____________ Simp

Class: Introduction to Logic
Write a natural deduction proof for the following deductive,
valid argument.
1. (A > Z) & (B > Y)
2. (A > Z) > A / Z v Y

Use integration to derive the formula for the area of an ellipse
with equation x^2/a^2+ Y^2/b2 = 1 (the symmetry of the ellipse
across the y and x-axes may be used in your solution without
proof).

1. For each statement that is true, give a proof and for each
false statement, give a counterexample
(a) For all natural numbers n, n2
+n + 17 is prime.
(b) p Þ q and ~ p Þ ~ q are NOT logically
equivalent.
(c) For every real number x
³ 1, x2£
x3.
(d) No rational number x satisfies
x^4+ 1/x
-(x+1)^(1/2)=0.
(e) There do not exist irrational numbers
x and y such that...

For each of the statements below, say what method of proof you
should use to prove them. Then say how the proof starts and how it
ends. Pretend bonus points for filling in the middle.
a. There are no integers x and y such that x is a prime greater
than 5 and x = 6y + 3.
b. For all integers n , if n is a multiple of 3, then n can be
written as the sum of...

4 Inference proofs
Use laws of equivalence and inference rules to show how you can
derive the conclusions from the given premises. Be sure to cite the
rule used at each line and the line numbers of the hypotheses used
for each rule.
a) Givens:
1 a∧b
2 c → ¬a
3 c∨d
Conclusion: d
b) Givens
1 p→(q∧r)
2 ¬r
Conclusion ¬p

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