Intuitively, an argument is valid if it applies correct laws of inference (e. g., Universal Modus Ponens, Universal Modus Tollens, Universal Transitivity) to its premises in order to obtain the next premise or the conclusion (the precise definition of validity is far more nuanced). If all premises in a valid argument are true, a valid argument always pro- duces a true conclusion. However, a valid argument could start with false premises or false premises could be interjected into its body ul- timately leading to a false conclusion. A valid argument in which all premises are true is called sound (an argument that is not valid cannot be sound). Determine two things about each of the below arguments arguments: a) whether it is valid, b) whether it is sound. When declar- ing an argument valid please state the inference law that was applied in it. When declaring an argument invalid specify which common mistake was made in it. (a) All people are sequoias All sequoias are immortal .. All people are immortal
(b) All dogs are carnivorous. Aaron is not a dog. .. Aaron is not carnivorous.
(c) All computer science professors know Python well. John knows Python well. .. John is a computer science professor.
(d) All massless particles can travel with velocity greater than the speed of light. Photon is a massless particle 2. Photon can travel with velocity greater than the speed of light.
(e) All stars with masses greater than 30 masses of the Sun live at most 3 million years. The North Star's age is greater than 50 billion years .. The North Star's mass is less or equal than 30 masses of the Sun
(f) All numbers whose sum of digits is a multiple of 3 are them- selves multiples of 3 The sum of digits of the number 1,333,333,333 is not a mul- tiple of 3 .. 1,333,333,333 is not a multiple of 3.