Question on rules of inference

  • Thread starter Thread starter cue928
  • Start date Start date
  • Tags Tags
    Rules
cue928
Messages
129
Reaction score
0

Homework Statement


What rule of inference is used with the following statement:
Kangaroos live in Australia and are marsupials. Therefore, kangaroos are marsupials.

I set this up as p = kangaroos live in Australia and q = kangaroos are marsupials. Therefore, p. To me, it looks like the "simplification" rule, but in our book, simplification is set up as:
p ^ q; therefore, p. Can I change how I defined p and q or am I wrong to begin with?
 
Physics news on Phys.org
cue928 said:

Homework Statement


What rule of inference is used with the following statement:
Kangaroos live in Australia and are marsupials. Therefore, kangaroos are marsupials.

I set this up as p = kangaroos live in Australia and q = kangaroos are marsupials. Therefore, p.
Therefore q.
cue928 said:
To me, it looks like the "simplification" rule, but in our book, simplification is set up as:
p ^ q; therefore, p. Can I change how I defined p and q or am I wrong to begin with?
If your hypothesis is p ^ q, the conclusion can be p or it can be q.

IOW,
p ^ q ==> q
and
p ^ q ==> p
 
Thank you.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Discrete Math implications by rules of inference
Replies
3
Views
1K
Direct Proof that every zero of p(T) is an eigenvalue of T
Replies
24
Views
3K
Truth Table Rules of Inference
Replies
6
Views
3K
Proving Conclusion of R: Using Rules of Inference and Given Premises
Replies
20
Views
2K
Proving Proposition: ##\forall x (P(x) \implies Q(x))##
Replies
2
Views
1K
Verify Green's Formula for a Simple DE
Replies
1
Views
1K
Probability Questions: Union, Intersection and Combinations
Replies
16
Views
2K
True or false questions about Divergence and Curl
Replies
1
Views
1K
Mixed random variables problem
Replies
6
Views
1K
Simplifying this derivative....
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top