Some Methods and Examples of Valid Reasoning

I. Euler diagram

Draw pictures (diagrams). If any diagram that satisfies the hypotheses contradicts the conclusion, the argument is not valid.

Hypotheses:
All roses are red.
This flower is a rose.

Conclusion:
This flower is red.


II. Direct reasoning

If the statement "if p then q" is true and p is true, then q must be true.

Hypotheses:
If you stay up late, you will be tired in the morning.
I stayed up late last night.

Conclusion:
I'm tired this morning.


III. Indirect reasoning

If the statement “ if p the q” is true and q is false, then p must also be false.

Hypotheses:
If you stay up late, you will be tired in the morning.
I’m not tired this morning.

Conclusion:
I did not stay up late last night.


IV. Chain rule

If the statements “if p then q” and “if q then r” are both true, then if p is true, r must also be true.

Hypotheses:
If I work hard, I earn lots of $$$.
If I earn lots of $$$, I pay high taxes.

Conclusion:
If I work hard then I pay high taxes.